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Volume of a rectangular prism

Here you will learn about the volume of a rectangular prism, including what it is and how to find it.

Students will first learn about the volume of a rectangular prism as part of geometry in 5 th grade. Students will expand on this knowledge in 6 th grade to include rectangular prisms with fractional dimensions.

Every week, we teach lessons on finding the volume of a rectangular prism to students in schools and districts across the US as part of our online one-on-one math tutoring programs. On this page we’ve broken down everything we’ve learnt about teaching this topic effectively.

What is volume of a rectangular prism?

The volume of a rectangular prism is the amount of space there is within it. Since rectangular prisms are 3 dimensional shapes, the space inside them is measured in cubic units.

\text{Volume of a rectangular prism }=\text { length } \times \text { width } \times \text { height }

For example,

This rectangular prism is made from 24 unit cubes – each side is 1 \, cm . That means the space within the rectangular prism, or the volume, is 24 \, \mathrm{cm}^3.

Even though you can’t see all 24 unit cubes, you can prove there are 24 by thinking about the rectangular prism in parts.

The bottom part of the prism is made up by 2 rows of 4 cubes – or 8 total cubes. The bottom part has a volume of 8 \, \mathrm{cm}^3 .

The other layers of the rectangular prism are exactly the same. Since the height is 3 \, cm , there are 3 layers of cubes. Each layer has a volume of 8 \, \mathrm{cm}^3 , so add them to find the total volume.

Thinking about this further, the volume of a rectangular prism is the area of the base times the height. Consider the same rectangular prism. If you were to hold it up and look at the bottom, it would look like this:

And the height of the prism is 3 \, cm , so 8 \, \mathrm{cm}^2 \times 3 \mathrm{~cm}=24 \mathrm{~cm}^3 .

This is why the formula for the volume of a rectangular prism is:

\text{Volume of a rectangular prism } = \text { length } \times \text { width } \times \text { height }

[FREE] Volume Of A Rectangular Prism Worksheet (Grade 6 to 12)

Use this worksheet to check your grade 6 to 12 students’ understanding of volume of a rectangular prism. 15 questions with answers to identify areas of strength and support!

Common Core State Standards

How does this relate to 5 th grade math and 6 th grade math?

• Grade 5 – Geometry (5.G.C.5b) Apply the formulas V=l \times w \times h and V=b \times h for rectangular prisms to find volumes of right rectangular prisms with whole number edge lengths in the context of solving real world and mathematical problems.
• Grade 6 – Geometry (6.G.A.2) Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l \times w \times h and V = b \times h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.

How to calculate the volume of a rectangular prism

In order to find the volume of a rectangular prism with cube units shown:

• Decide how many cubes make up the first layer.
• Find the total of all the layers.

Write the answer and include the units.

In order to calculate the volume of a rectangular prism with the formula:

Write down the formula.

Substitute the values into the formula.

Solve the equation.

Volume of a rectangular prism examples

Example 1: volume of a rectangular prism.

Each cube has a side length of 1 \, inch . Find the volume of the rectangular prism.

If you picked up the prism and looked at the bottom, you would see a 9 by 2 rectangle:

The bottom layer of the rectangular prism is 9 by 2 cubes, so it is made up of 18 inch cubes or 18 \text { inches}{ }^3.

2 Find the total of all the layers.

The height is 2 \, inches , so there are 2 layers of cubes.

Since each layer has a volume of 18 \text { inches}^3 , you can add the volume of each layer to find the total volume.

\begin{aligned} \text { Volume } & = 18 \, \text {inches}^3 + 18 \, \text {inches}^3 \\\\ & = 36 \, \text {inches}^3\end{aligned}

You can also multiply the area of the base ( \text {length } \times \text { width} ) times the \text { height} .

\begin{aligned} \text { Volume } & =18 \text { inches}^2 \times 2 \text { inches } \\\\ & =36 \text { inches}^3 \end{aligned}

3 Write the answer and include the units.

The dimensions of the rectangular prism are in inches, therefore the volume is in cubic inches ( \text { inches}^3. )

\text { Volume }=36 \text { inches}^3

Example 2: volume of a cube

Calculate the volume of this cube.

\text {Volume }=\text { length } \times \text { width } \times \text { height }

Since this is a cube, the length of the rectangular prism, width of the rectangular prism, and height of the rectangular prism are all 6 \,ft :

\text {Volume }=6 \times 6 \times 6

\begin{aligned} & \text {Volume }=6 \times 6 \times 6 \\\\ & \text {Volume }=216 \end{aligned}

The dimensions of the rectangular prism are in feet, therefore the volume is in cubic feet ( ft^3 ).

\text {Volume }=216 \, \mathrm{ft}^3

Example 3: volume of a rectangular prism – different units

Calculate the volume of this rectangular prism.

Notice here that one of the units is in cm and the others are in m . All the units should be the same to calculate the volume.

Change cm to m : 50 \,cm = 0.5 \,m .

Now that all of the measurements are in m, calculate the volume:

\text {Volume }=4 \times 2 \times 0.5

\begin{aligned} & \text {Volume }=4 \times 2 \times 0.5 \\\\ & \text {Volume }=4 \end{aligned}

Since the dimensions of the rectangular prism were calculated in meters, the volume is in cubic meters.

\text {Volume }=4 \, m^3

Example 4: volume of a rectangular prism – fractions

\text {Volume }=9 \times 13 \, \cfrac{2}{3} \, \times 5 \, \cfrac{3}{4}

\begin{aligned} \text {Volume } & =9 \times 13 \, \cfrac{2}{3} \, \times 5 \, \cfrac{3}{4} \\\\ & =\cfrac{9}{1} \, \times \, \cfrac{41}{3} \, \times \, \cfrac{23}{4} \\\\ & =\cfrac{8,487}{12} \\\\ & =707 \, \cfrac{3}{12} \text { or } 707 \, \cfrac{1}{4} \end{aligned}

V=707 \, \cfrac{1}{4} \, f t^3

Example 5: find the length of a rectangular prism given the volume

The rectangular prism below has a square base.

The height of the rectangular prism is 8 \, \cfrac{2}{9} \, m and the volume of the rectangular prism is 33 \, \mathrm{m}^3 .

Find the area of the base.

The volume of the rectangular prism is 33 \, \mathrm{m}^3 and the height is 8 \, \cfrac{2}{9} \, m – fill those into the formula.

\begin{aligned} & 33=l \times w \times 8 \, \cfrac{2}{9} \\\\ & 33=(\text {area of the base}) \times 8 \, \cfrac{2}{9} \end{aligned}

To find the missing area, you can divide 33 by 8 \, \cfrac{2}{9} :

\begin{aligned} & 33 \, \div 8 \, \cfrac{2}{9} \\\\ & =33 \, \div \, \cfrac{74}{9} \\\\ & =\cfrac{33}{1} \, \times \, \cfrac{9}{74} \\\\ & =\cfrac{297}{74} \\\\ & =4 \, \cfrac{1}{74} \end{aligned}

Since the area of the base is calculated by \text {length } \times \text { width} , the measurement is 2D and the units are squared.

The area of the base is 4 \, \cfrac{1}{74} \, m^2.

Example 6: dimensions of a cube given the volume

Find the dimensions of a cube that has a volume of 64 \, \mathrm{mm}^3 .

The only value known is the volume which is 64 \, \mathrm{mm}^3 – fill it into the formula.

64=l \times w \times h

Since the shape is a cube, the length, width and height are all the same. The missing number, when multiplied by itself three times, makes 64 .

Since 64 is even, the number multiplied will also be even. It will also be much smaller than 64 , since it was multiplied 3 times by itself to get to 64 .

With this in mind, start guessing and checking with smaller, even numbers.

Let’s try 2 …

2 \times 2 \times 2=8

Let’s try 4 …

4 \times 4 \times 4=64

The dimensions of the cube are 4 \, \mathrm{mm} \times 4 \, \mathrm{mm} \times 4 \, \mathrm{mm}.

Teaching tips for volume of rectangular prism

• In the beginning, focus on activities and discussions that show the units (cubes) within rectangular prisms and connect such representations to the volume formula.
• Worksheets are easy ways to provide practice problems but be sure to include ones that include word problems or real-life applications of volume.

Easy mistakes to make

• Writing the incorrect units or forgetting to include the units Always include units when recording a measurement. Volume is measured in cubic units. For example, \mathrm{mm}^3, \mathrm{~cm}^3, \mathrm{~m}^3 etc.

• Calculating surface area instead of volume Surface area and volume are different types of measurement – surface area is the total area of the faces and is measured in square units, and volume is the space within the shape and is measured in cubic units.

Related volume lessons

• Volume of a cylinder
• Volume of a hemisphere
• Volume of a sphere
• Volume of a cone
• Volume of a triangular prism
• Volume of a pyramid
• Volume of square pyramid
• Volume formula
• Volume of a prism
• Volume of a cube

Practice volume of a rectangular prism questions

1. Each cube has a side length of 1 \, ft . Find the volume of the rectangular prism.

If you picked up the prism and looked at the bottom, you would see a 6 by 4 rectangle:

The bottom layer of the rectangular prism is 6 by 4 cubes, so it is made up of 24 feet cubes or 24 \, \text {ft}^3.

The height is 4 \, feet , so there are 4 layers of cubes. Since each layer has a volume of 24 \, \text {ft}^3 , you can add the volume of each layer to find the total volume.

\begin{aligned} \text {Volume } & =24 \, f t^3+24 \, f t^3+24 \, f t^3+24 \, f t^3 \\\\ & =96 \, f t^3 \end{aligned}

You can also multiply the area of the base ( \text {length } \times \text { width} ) times the \text {height} .

\begin{aligned} \text {Volume } =24 \, \mathrm{ft}^2 \times 4 \, f t \\\\ & =96 \, \mathrm{ft}^3 \end{aligned}

2. Calculate the volume of the rectangular prism.

\begin{aligned} \text{Volume }&= \text{ length }\times \text{ width }\times \text{ height } \\\\ \text{Volume }&= 12 \times 3 \times 4 \\\\ \text{Volume }&= 144 \, \mathrm{cm}^{3} \end{aligned}

3. Calculate the volume of this rectangular prism.

There are measurements in cm and m , so convert the units before calculating the volume: 380 \, cm to 3.8 \, m .

\begin{aligned} \text{Volume }&= \text{ length }\times \text{ width }\times \text{ height }\\\\ \text{Volume }&= 2.3 \times 2 \times 3.8 \\\\ \text{Volume }&=17.48 \,\mathrm{m}^{3} \end{aligned}

Since the measurements used were in meters, the volume will be in cubic meters.

4. The volume of this rectangular prism is 600 \, cm^{3} . Find the height of the rectangular prism.

Fill in the known values:

\begin{aligned} & 600=8 \times 25 \times h \\\\ & 600=200 \times h \end{aligned}

The missing height times 200 is equal to 600 , so h=3 \, \mathrm{cm} because 200 \times 3=600 .

5. Calculate the volume of the rectangular prism.

\begin{aligned} & \text {Volume }=\text { length } \times \text { width } \times \text { height } \\\\ & \text {Volume }=11 \, \cfrac{3}{4} \, \times 4 \, \cfrac{1}{3} \, \times 3 \, \cfrac{2}{3} \\\\ & \text {Volume }=\cfrac{47}{4} \, \times \, \cfrac{13}{3} \, \times \, \cfrac{11}{3} \\\\ & \text {Volume }=\cfrac{6,721}{36} \\\\ & \text {Volume }=186 \, \cfrac{25}{36} \, \mathrm{ft}^3 \end{aligned}

6. The base of this prism is a square. The volume of the prism is 450 \, \mathrm{cm}^{3} . Find the height of the prism.

Since the base of the prism is a square, the length and the width are both 10 \, cm .

\begin{aligned} & \text {Volume }=\text { length } \times \text { width } \times \text { height } \\\\ & 450=10 \times 10 \times h \\\\ & 450=100 \, h \end{aligned}

The missing height times 100 is equal to 450 , so h=4.5 \, \mathrm{cm} because 100 \times 4.5=450 .

Volume of a rectangular prism FAQs

A cuboid is a three-dimensional shape with 6 rectangular faces, 8 vertices, and 12 edges. It is another name for a rectangular prism.

Volume of a rectangular prism is the area of the base (length times width) times the height of the rectangular prism or l \times w \times h .

No, but the formula for both can be stated as the \text {area of the base } \times \text {height of the prism} . However, since there are different formulas for finding the area of a rectangle and finding the area of a triangle, they are not found with the exact same formula.

Find the area of the six faces and then add them together.

The next lessons are

• Surface area
• Pythagorean theorem
• Trigonometry

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Volume of Rectangular Prism Word Problems Worksheets

Related Pages Math Worksheets Lessons for Fifth Grade Free Printable Worksheets

Printable “Volume of Rectangular Prisms” Worksheets: Volume of Rectangular Prisms Volume of Composite Rectangular Prisms Volume of Rectangular Prisms Word Problems

In these free math worksheets, you can practice how to solve word problems that involve the volumes of rectangular prisms. You can either print the worksheets (pdf) or practice online.

How to solve volume of rectangular prisms word problems?

Solving word problems that involve the volume of rectangular prisms involve using the formula for volume and interpreting the information given in the word problem.

• Read the problem carefully and identify what it’s asking for. This could be the total volume of a rectangular prism, the missing dimension (length, width, or height) given the volume and other two dimensions, or the amount of material needed to fill the prism.
• Look for numbers or measurements mentioned in the problem. These might represent the length, width, height, or volume of the rectangular prism.
• Pay attention to words that indicate the dimensions of the prism (length, width, height), or the volume itself (volume, cubic units, capacity).
• Apply the volume formula: The volume of a rectangular prism is calculated by multiplying the length (l), width (w), and height (h) of the prism. The formula is: Volume = l × w × h.
• If the problem involves finding a missing dimension or solving a multi-step process, you can set up an equation using variables to represent the unknown values.
• Solve the equation or perform the calculation: Substitute the known values (dimensions or volume) into the formula or equation and solve for the unknown variable (missing dimension). If the problem asks about the amount of material needed, you might need to calculate the surface area (depending on whether the entire prism needs to be covered) and relate it to the material required (e.g., paint needed to coat the entire box).
• Interpret the answer: Double-check your calculations for accuracy. Ensure your answer is in the appropriate unit (cubic units for volume

Click on the following worksheet to get a printable pdf document. Scroll down the page for more Volume of Rectangular Word Problems Worksheets .

More Volume of Rectangular Prism Word Problems Worksheets

Printable (The answers are on the second page) Volume of Rectangular Prism Worksheet #1 Volume of Rectangular Prism Worksheet #2 Volume of Rectangular Prism Worksheet #3 Volume of Rectangular Prism Worksheet #4

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Volume of Rectangular Prism Word Problems Volume of Rectangular Prism Lesson

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Volume of a Rectangular Prism Worksheets

Try our engaging volume of rectangular prisms worksheets for grade 5, grade 6, and grade 7, and bolster skills in finding the volume in a step-by-step approach beginning with counting cubes, moving to finding volume of cubes followed by problems to find the volume using area and height expressed as integers, decimals and fractions. Practice finding the volume of L-blocks, convert between units and find the missing parameters as well. Kick-start your preparation with our free worksheets!

Volume of Rectangular Prisms | Integers

Introduce students to find the volume of rectangular prisms with these printable worksheets, presenting the base area and length of the prism as integers. Plug them in V=Base area*height to find the volume.

• Download the set

Volume of Rectangular Prisms | Decimals

Packed here are ample problems to find the volume of rectangular prisms whose base area and one side measure are decimals. Use the known values to work out the volume.

Volume of Rectangular Prisms | Using Side lengths

Instruct 5th grade and 6th grade students to identify the three attributes height, length and width indicated on the rectangular prism and multiply the three to figure out the volume. Easy level deals with values ≤ 20 while moderate level has values ≥ 20.

Volume of Rectangular Prisms | Sides - Decimals

Plug in the measures of the length, height and width expressed as decimals in the formula V=l*w*h and find the volume of each rectangular prism in this set of pdf worksheets.

Volume of Rectangular Prisms | Sides - Fractions

Solve this set of printable volume of rectangular prisms worksheets whose side measures are denoted as fractions. Change the mixed fractions to improper fractions, multiply l*w*h to compute the volume of the prisms.

Volume of Rectangular Prisms | Unit conversion

The dimensions are expressed in different units. Make the units uniform by converting them to the one specified in the answer and then multiply the three to find the volume of the rectangular prisms.

Volume of L-Blocks

Decompose the L-blocks into non-overlapping rectangular prisms and find their volume in these pdf worksheets for grade 6 and grade 7, offering two levels of difficulty classified as easy and moderate based on the range of numbers used.

Volume of L-Blocks | Decimals

Raise the bar with this array of 7th grade worksheets, where the dimensions are expressed as decimals. Split the L-block, determine the volume of individual prisms, sum them up to compute the volume of the L-blocks.

Finding the missing measure

The volume and any two of the three dimensions (height, length or width) are specified. Direct students to rearrange the formula, making the missing measure the subject, assign the known values and solve.

Counting Cubes to find the Volume

Familiarize students with the basics of volume as they begin counting the cubes to determine the volume of each rectangular prism and/or solid block. Practice drawing prisms using the given dimensions as well.

(24 Worksheets)

Volume of Cubes

Catering to the needs of grade 5 through grade 7 children, these volume worksheets add on to your practice in determining the volume of cubes. The dimensions are expressed as integers, decimals and fractions.

(15 Worksheets)

Related Worksheets

» Volume of Triangular Prisms

» Volume of Prisms

» Volume of Rectangular Pyramids

» Volume of Cylinders

» Volume of Composite Shapes

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Volume of Rectangular Prism

The volume of a rectangular prism is the measurement of the total space inside it. Imagine a rectangular container filled with water. In this case, the total quantity of water that the container can hold is its volume. A prism is a polyhedron having identical bases, flat rectangular side faces, and the same cross-section all along its length. Prisms are classified on the basis of the shape of their base. A rectangular prism is categorized as a three-dimensional shape. It has six faces and all the faces of the prism are rectangles. Let us learn the formula to find the volume of a rectangular prism in this article.

What is the Volume of Rectangular Prism?

The volume of a rectangular prism is defined as the space occupied within a rectangular prism . A rectangular prism is a polyhedron that has two pairs of congruent and parallel bases. It has 6 faces (all are rectangular),12 sides, and 8 vertices. As the rectangular prism is a three-dimensional shape (3D shape) , the unit that is used to express the volume of the rectangular prism is cm 3 , m 3 and so on. In mathematics, any polyhedron , having all such characteristics can be referred to as a Cuboid.

Volume of Rectangular Prism Formula

The formula for the volume of a rectangular prism = base area × height of the prism. Since the base of a rectangular prism is a rectangle, its area will be l × w. This area is then multiplied by the height of the prism to get the volume of the prism. Therefore, another way to express this formula is by multiplying the length, width, and height of the prism and write the value in cubic units (cm 3 , m 3 , in 3 , etc).

Therefore, the formula for the volume of a rectangular prism is, volume of a rectangular prism (V) = l × w × h, where

• “l” is the base length
• “w” is the base width
• “h” is the height of the prism

To find the volume of the rectangular prism, we multiply the length, width, and height, that is the area of the base is multiplied by the height. It should be noted that the volume is measured in cubic units.

There are two types of rectangular prisms - right rectangular prisms and oblique prisms.

• In the case of a right rectangular prism, the bases are perpendicular to the other faces.
• In the case of an oblique rectangular prism, the bases are not perpendicular to the other faces. Thus, the perpendicular drawn from the vertex of one base to the other base of the prism will be taken as its height.

It should be noted that we can apply the same formula to calculate the volume of the prism, that is the rectangular prism volume formula, v = lwh, irrespective of the type of rectangular prism.

How to Find the Volume of a Rectangular Prism?

Before calculating the volume of a rectangular prism using the formula, we need to make sure that all the dimensions are of the same units. The following steps are used to calculate the volume of a rectangular prism.

• Step 1: Identify the type of the base and find its area using a suitable formula (as explained in the previous section).
• Step 2: Identify the height of the prism, which is perpendicular from the top vertex to the base of the prism.
• Step 3: Multiply the base area and the height of the prism to get the volume of the rectangular prism in cubic units. Volume = base area × height of the prism

Example: Calculate the volume of a rectangular prism whose height is 8 in and whose base area is 90 square inches.

Solution: We can calculate the volume of the rectangular prism using the following steps:

• Step 1: The base area is already given as 90 square inches.
• Step 2: The height of the prism is 8 in.
• Step 3: The volume of the given rectangular prism = base area × height of the prism = 90 × 8 = 720 cubic inches.

Volume of Rectangular Prism Examples

Example 1: If the volume of a rectangular prism is 40 cubic units and its base area is 10 square units, what is its height?

Solution: Given, the volume of the rectangular prism = 40 cubic units; and the base area of the rectangular prism= l × b = 10 square units.

Using the volume of rectangular prism formula, base area × height of the prism = 40 The height of the given rectangular prism = 10 × height = 40.

Thus, the height of the rectangular prism = 40/10 = 4 units

Example 2: If the base length of a rectangular prism is 8 inches, the base width is 5 inches and the height of the prism is 16 inches, find the volume of the rectangular prism.

Solution: Given: The base length of the rectangular prism (l) = 8 in, base width (w) = 5 in.

So the base area = l × w = 8 × 5 = 40 sq inches. The height of the prism is h = 16 in.

Using the volume of the rectangular prism formula, the volume of rectangular prism = base area × height of the prism = (40 × 16) = 640 cubic inches.

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Practice Questions on Volume of Rectangular Prism

Faqs on volume of rectangular prism, what is the volume of a rectangular prism.

The volume of a rectangular prism is the capacity that it can hold or the space occupied by it. Thus, the volume of a rectangular prism can be calculated by multiplying its base area by its height. The formula that is used to find the volume of a rectangular prism is, Volume (V) = height of the prism × base area. It is expressed in cubic units such as cm 3 , m 3 , in 3 , etc.

What is the Formula for the Volume of a Rectangular Prism?

The formula for the volume of a rectangular prism is, Volume (V) = base area × height of the prism. Another way to express this formula is, Volume = l × w × h; where 'l' is the length, 'w' is the width, and 'h' is the height of the prism.

In order to find the volume of a rectangular prism, follow the steps given below:

• Step 1: Identify the length (l) and width (w) of the base of the prism.
• Step 2: Find the height (h) of the prism.
• Step 3: Substitute the respective values in the formula, V = lwh
• Step 4: Find the product of these values to get the volume of the prism in cubic units.

How to Find the Height of a Rectangular Prism when the Volume of a Rectangular Prism is given?

The height of a rectangular prism can be calculated if the volume of the prism is given using the same formula, Volume (V) = base area × height of the prism. For example, the volume of a prism is 600 cubic units and its base area is 60 square units. Then, after substituting the values in the equation, we get 600 = 60 × height of the prism. This means, height = 600/60 = 10. Therefore, the height is 10 units.

What Happens to the Volume of Rectangular Prism if its Height is Doubled?

We know that the volume of a rectangular prism is the product of its three dimensions, that is, volume = length × width × height. If its height is doubled, its volume will be l × w × (2h) = 2lwh = 2 × v. Thus, we can say that the volume of the rectangular prism also gets doubled when its height is doubled.

What Happens to the Volume of Rectangular Prism if the Length is Doubled and the Height is Reduced to One Half?

The formula for calculating the volume of a rectangular prism is volume = length × width × height. If its length is doubled, and the height is reduced to half, then its volume can be written as, V = (2l) × (w) × (1/2h). After simplifying this, we get l × w × h which is the regular formula for volume. Thus, we can say that the volume of the rectangular prism will remain the same if its length gets doubled and the height is reduced to half.

What Happens to the Volume of Rectangular Prism if the Length, Width, and Height of Prism are Doubled?

The volume of a rectangular prism is the product of its three dimensions, that is volume = length × width × height. If its length, width, and height is doubled, then its volume will be (2l) × (2w) × (2h) = 8lwh = 8 × v. Thus, we can conclude that if its length, width, and height is doubled, the volume of the rectangular prism will be 8 times the original value.

How to Find the Volume of a Rectangular Prism with Fractions?

The volume of a rectangular prism can be calculated even if the values are given in fractions . For example, if the length of a rectangular prism is \(1\dfrac{3}{5}\) units, the width is 3/4, and its height is 2/3 units, the volume of the prism = l × w × h = \(1\dfrac{3}{5}\) × 3/4 × 2/3. Now, let us convert the mixed fraction into an improper fraction and then multiply all the fractions. We will first multiply the numerators and then the denominators and then reduce the resultant fraction, if needed. This means Volume = 8/5 × 3/4 × 2/3 = 48/60 = 4/5. Therefore the volume of the prism is 4/5 cubic units.

Volume of a Rectangular Prism Calculator

What is a rectangular prism, what is the formula for the volume of a rectangular prism, how to find the volume of a rectangular prism.

With this volume of a rectangular prism calculator – a.k.a., a box volume calculator – you'll find the volume of any box-shaped container in a blink of an eye. No fuss is required. You need to enter only three values, and we'll calculate the volume for you (though it's not so tricky, you could figure it out yourself 😊).

If you're searching for the definition, check the section What is a rectangular prism . However, if you're still wondering how to find the volume of a rectangular prism, we'll show you step-by-step how to use our calculator on an (almost) real-life example – the volume of a cat 🐈.

If you're looking for the area of a rectangular prism, try our surface area of a rectangular prism calculator , or go to the rectangular prism calculator for an all-in-one rectangular prism tool.

A rectangular prism is a 3D shape with 6 faces, all of which are rectangles . Other names for a rectangular prism are a cuboid , or simply a box .

Every rectangular prism has:

• 8 vertices;
• 12 edges; and

Finding the volume of a rectangular prism is a straightforward task – all you need to do is to multiply the length, width, and height together:

Rectangular prism volume = length × width × height

Where can you use this formula in real life? Let's imagine three possible scenarios:

You bought a fish tank for your golden fish 🐠. It's in a regular box shape, nothing fancy, like a corner bow-front aquarium. If you're wondering how much water you need to fill it, simply use the volume of a rectangular prism formula. It is a similar story for other pets kept in tanks and cages, like turtles or rats – if you want a happy pet, then you should guarantee them enough living space.

The time has come – you've decided that this year you'd like to grow your own carrots 🥕 and salad 🥗. For that, you need to construct a raised bed and fill it with potting soil. But how much dirt should you buy? Well, that's the same question as how to find the volume of a rectangular prism: measure your raised bed, use the formula, and run to the gardening center.

You are going on the vacation of your dreams 🌴. You have to pack your stuff for the three weeks, and you're wondering which suitcase 🧳 will fit more in :

Your good old large suitcase, 30 × 19 × 11 inches; or

The new fancy one, 28 × 21 × 12 inches

That's again the problem solved by the volume of a rectangular prism formula. Solve it manually, or find it using our calculator.

If you're searching for a calculator for other 3D shapes – like e.g. a cube , which is a special case of a rectangular prism – you may want to check out our comprehensive volume calculator . It has a gazillion different shapes! (Fourteen, to be exact.)

Well, now that you know what a rectangular prism is and its volume formula, all the calculations should be a piece of cake! Just measure the three dimensions of your rectangular prism, and use the method from the previous paragraph. Alternatively, you can simply use our box volume calculator.

So, let's have a look at the example – let's calculate the volume of a cat🐈. Yes, a cat, as cats are almost like liquids (they take on the shape of whatever container they are in). Assuming that the cat completely fills a plastic container with dimensions 12 inches × 10 inches × 8 inches:

Input the container's length into the first field of our volume of a rectangular prism calculator. It's 12 inches in our case.

Enter the width of the box . Put 10 inches into the proper field.

Finally, input the height of your container, 8 inches.

And there it is: the volume of a rectangular prism calculator did the job. Now we know that our cat's volume is 960 cubic inches . Isn't that paw esome? 🐾

(Of course, it's a really rough estimate. Take it with a pinch of salt 🧂 or even two pinches.)

So, now that you know your cat's volume, you can go and search for a perfect cardboard box📦 for your pet!

How do I calculate the volume of a rectangular prism?

To find the volume of a rectangular prism, you need to:

• Determine the lengths of the sides : width, length, and height.
• Multiply together the three values from Step 1.
• The result you've got is the volume of your solid.

Don't forget to include the units if it is given! Since it's volume, you need cubic units.

What is the volume of a rectangular prism with sides 2, 5, and 7?

The answer is 70 . To see how to get this result, recall the formula for the volume of a rectangular prism:

volume = length × height × width

Hence, we compute the volume as 2 × 5 × 7 = 70 .

Remember to include the units: for instance, if your measurements are in inches (in), the volume will be in cubic inches (in³).

How do I calculate the volume of a rectangular prism given diagonals?

To determine the volume of a rectangular prism when you know the diagonals of its three faces, you need to apply the formula:

volume = 1/8 × √(a² - b² + c²)(a² + b² - c²)(-a² + b² + c²) ,

where a, b, and c are the diagonals you're given. This formula can be easily derived by using the Pythagorean theorem.

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Formula Volume of a Rectangular Prism

How to find the volume of a rectangular cylinder.

This page examines the properties of a rectangular prism such as the image above. A rectangular prism is exactly what it sounds like . It's a 3 dimensional shape with a width, height and a length (or base) such as the 3,2, and 8 this picture .

Rectangular Prism Volume Formula

Practice Problems on Volume of a Rectangular Prism

What is the volume of the rectangular prism with the dimension shown below?

Use the formula for the volume of a cylinder as shown below.

$ V = 2 \cdot 5 \cdot 3 \\ V = 30 $

If the volume of a rectangular prism is 30" 3 and its height is 5", its length is 2", what is its width?

$$ volume = l \cdot w \cdot h \\ 30 = 5 \cdot 2 \cdot w \\ 30 = 10 \cdot w \\ width = \frac{30}{10} = 3\text{"} $$

The volume of a rectangular prism is 125" 3 and its height is 5". Is it possible for all 3 of its dimensions (base, height, width) to be the exact same measurement? Explain.

$$ 5^3 = 125 \\ volume = length \cdot width \cdot height \\ 125 = 5 \cdot 5 \cdot 5 $$

Rectangular prism A has the following dimensions: 2" width, 3" height and 6" base (ie length). On the other hand, rectangular prism B has these dimensions: 1" width, 3" height and 7" base (or length).

Which prism has a greater volume?

$$ \\ volume = length \cdot width \cdot height \\ V = 2 \cdot 3 \cdot 6 = \color{red}{36 \text{ in}^3 } $$

$$ volume = length \cdot width \cdot height \\ V = 1 \cdot 3 \cdot 7 = 21\text{ in}^3 $$

Answer: Prism A

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How to Calculate the Volume of a Rectangular Prism

Last Updated: August 14, 2024 Fact Checked

• Finding Volume
• Using Cube Units
• Sample Problems
• Common Mistakes

What is a rectangular prism?

• Other Volume Formulas
• Practice Worksheets

This article was reviewed by Grace Imson, MA and by wikiHow staff writer, Sophie Burkholder, BA . Grace Imson is a math teacher with over 40 years of teaching experience. Grace is currently a math instructor at the City College of San Francisco and was previously in the Math Department at Saint Louis University. She has taught math at the elementary, middle, high school, and college levels. She has an MA in Education, specializing in Administration and Supervision from Saint Louis University. There are 10 references cited in this article, which can be found at the bottom of the page. This article has been fact-checked, ensuring the accuracy of any cited facts and confirming the authority of its sources. This article has been viewed 1,292,553 times.

Volume is the amount of three-dimensional space taken up by an object. The computer or phone you're using right now has volume, and even you have volume! Finding the volume of a rectangular prism is actually really easy. Just multiply the length, the width, and the height of the rectangular prism or box that you want the volume of. That's all you have to do! But, this article will walk you through every step of this calculation, including what to do if you don’t know the dimensions of the prism. Calculators at the ready!

Volume of a Rectangular Prism: Formula

Calculate the volume of a rectangular prism by multiplying its width, length, and height together (in any order). Make sure all units are the same across the dimensions, then plug them into the formula Volume = W x L x H .

Finding the Volume of a Rectangular Prism (With Known Dimensions)

• The length is the longest side of the flat surface of the rectangle on the top or bottom of the rectangular prism. [1] X Research source
• The width is the shorter side of the flat surface of the rectangle on the top or bottom of the rectangular prism. [2] X Research source
• The height is the part of the rectangular prism that rises up. Imagine that the height is what stretches up a flat rectangle until it becomes a three-dimensional shape.
• For example , your box may have these dimensions: length (l) = 5 inches, width (w) = 4 inches, and height (h) = 3 inches.

• For example , let’s say that your rectangular prism has the dimensions length (l) = 5 inches, width (w) = 4 inches, and height (h) = 3 inches.
• To calculate this rectangular prisms volume, multiply 5 x 4 x 3 = 60 . The volume of this box is 60 .
• These numbers can be calculated in any order. For instance, multiplying 3 x 5 x 4 would produce the same final value of 60.
• Then, write the number value of your volume, followed by that measurement with the exponent 3 attached to it.
• For example , the rectangular prism in our example has its dimensions stated in inches. Therefore, our final answer with units would be Volume = 60 in 3 .

Finding the Volume of a Rectangular Prism (With Cube Units)

• Start by making note of the given side length of each small cube inside the rectangular prism.
• In our example , we’ll say that each of the cubes in the prism has a side length of 1 inch .

• For example , our rectangular prism has a 9 cubes on its long side and 2 cubes on its short side.
• If you’re struggling to visualize this process by counting cubes on the 3-dimensional shape, imagine what it would look like if you picked up the prism and looked at the bottom. What would the dimensions of that bottom rectangle be?
• In our example , you would see a 9 by 2 rectangle.
• If you have MathLink Cubes or something similar on hand, it may be helpful to physically build your prism out of cubes to better visualize it and its dimensions.

• For example , our rectangular prism has cubes with a side length of 1 inch, and there are 9 cubes on the long side of the rectangle. Therefore, our prism’s length = 1 inch x 9 = 9 inches .
• For example , our rectangular prism has cubes with a side length of 1 inch, and there are 2 cubes on the long side of the rectangle. Therefore, our prism’s length = 1 inch x 2 = 2 inches .

• For example , in a rectangular prism with a bottom layer whose dimensions are 9 inches (length) by 2 inches (width) by 1 inch (height), you’d calculate Volume = 9 x 2 x 1 = 18 .
• Since our original cube side-length was given in inches and volume is always measured in cubic units, our bottom layer’s final volume with units would be Volume = 18 inches 3

• For example , let’s say that our rectangular prism has 2 layers of cubes.
• Since we already know that the bottom layer has a volume of 18 inches 3 , all we have to do is add that value together 2 times .
• Therefore, the total volume of the rectangular prism is 18 inches 3 + 18 inches 3 = 36 inches 3

• If your original units were in inches : in 3
• If your original units were in centimeters : cm 3
• If your original units were in feet : ft 3
• In our example , the original units were given in inches, making our final answer 36 in 3 .

Practice Questions for Rectangular Prism Volume

• Write down the formula for the volume of a rectangular prism: Volume = length x height x width, or V = l x h x w.
• Plug your dimensions into the formula : Volume = 6 x 8 x 10.
• Solve the formula through multiplication: V = 480.
• Add cubic units to match the original units (in this case, inches): V = 480 inches 3 .
• The final volume of this rectangular prism is 480 inches 3 .
• Identify the length, width, and height of the cube : Cubes have faces and sides that are all equal to each other. Therefore, the side length of the cube being 6 feet means that all of the cubes side lengths (including length, width, and height) are 6 feet.
• Plug your dimensions into the formula : Volume = 6 x 6 x 6.
• Solve the formula through multiplication: V = 216.
• Add cubic units to match the original units (in this case, feet): V = 216 feet 3 .
• The final volume of this rectangular prism is 216 feet 3 .
• Convert your dimensions into the same units : Note that all dimensions must be in the same unit before calculating the volume of a rectangular prism. [9] X Research source Since our height is given in centimeters (not meters), we must convert this number into meters before continuing:
• 50 centimeters = 0.5 meters.
• If you can’t convert units off of the top of your head, use a unit conversation calculator .
• Plug your adjusted dimensions into the formula : Volume = 4 x 2 x 0.5.
• Solve the formula through multiplication: V = 4.
• Add cubic units to match the original units (in this case, meters): V = 4 meters 3 .
• The final volume of this rectangular prism is 4 meters 3 .

Common Mistakes When Solving for Volume

• If you’re studying for a test , it may be best to memorize the unit conversions you’ll need for your exam.
• Otherwise, however, you can always use a unit converter calculator to fix your units.

• The difference in numbers only has to do with the differing units—not because the actual volume of the prism has changed.
• Consider if you had a cardboard box in front of you. You could use a ruler to measure that box in inches or a measuring tape to measure it in feet. You would get a different answer, but the size of the box wouldn’t actually change.

• A cube is also a type of rectangular prism.

More Formulas for Volume & Rectangular Prisms

• Calculate the Area of a Rectangle : A = width (w) x length (l)
• Find the Surface Area of a Rectangular Prism : SA = 2(wl+hl+hw)
• Calculate Volume of a Prism : V = B (base) x h (height)
• Calculate Volume of a Cube : V = a 3 , where a = edge
• Calculate Volume of a Triangular Prism : V = 0.5 x B x h x l

Frequently Asked Questions About Volume & Rectangular Prisms

• For instance, say you bought a box-shaped fish tank. If you want to know how much water you need to fill that tank, use the rectangular prism volume formula.
• In another example, you may want to construct a raised garden bed and fill it with potting soil. To know how much potting soil you’ll need, plug the dimensions of your bed into the rectangular prism volume formula.
• Or, maybe you’re going on a dream vacation and need to choose between two suitcases. If you want to know which suitcase would fit more inside it, calculate the volume of each one and see which number value is largest.
• For example, if you know that the volume of a prism is 200 cubic units and the base area is 20 square units, then plug those values into the equation.
• Then, you’ll have the formula 200 = 20 x h .
• To solve for h , divide both sides of the equation by 20 to be left with 10 = h .
• Therefore, the height of the rectangular prism is 10 units !
• To explain this result, consider the original formula for the volume of a rectangular prism: V = length x width x height.
• If all of the dimensions are doubled, the volume will then be (2l) x (2w) x (2h) = 8lwh = 8 x V.
• As a result, the volume will be 8 x V, or 8 times its original value.

Volume of a Rectangular Prism Practice Worksheets

Community Q&A

• In the United States public school system, calculating the volume of a rectangular prism is typically first taught as a math skill in the 5th grade (according to Common Core State Standards). Then, it’s reinforced and expanded upon in 6th grade. [14] X Research source Thanks Helpful 0 Not Helpful 0
• If you’re teaching a student how to calculate the volume of a rectangular prism, try to focus on activities that show the cube units within a rectangular prism so that the student can really understand why volume is calculated the way it is. Be sure to also teach real-life applications for this problem to students. Thanks Helpful 0 Not Helpful 0

You Might Also Like

• ↑ http://www.softschools.com/math/geometry/topics/volume_of_a_rectangular_prism/
• ↑ https://www.khanacademy.org/math/cc-fifth-grade-math/5th-volume/volume-word-problems/a/volume-of-rectangular-prisms-review
• ↑ https://collected.jcu.edu/cgi/viewcontent.cgi?referer=&httpsredir=1&article=1032&context=mastersessays
• ↑ https://flexbooks.ck12.org/cbook/ck-12-interactive-middle-school-math-7-for-ccss/section/6.9/primary/lesson/volume-of-cubes-and-rectangular-prisms-4424741-msm7-ccss/
• ↑ https://www.avc.edu/sites/default/files/studentservices/lc/math/volumes.pdf
• ↑ https://www.ohlone.edu/mathmods/mathmod8
• ↑ https://byjus.com/maths/surface-areas-volumes/
• ↑ https://amsi.org.au/ESA_middle_years/Year6/Year6_2cT/Year6_2cT_R1_pg2.html
• ↑ https://www.geeksforgeeks.org/how-to-calculate-the-volume-of-a-rectangular-prism/
• ↑ https://www.thecorestandards.org/Math/Content/5/MD/

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1. Find the length, width, and height of the rectangular prism. 2. Multiply the length, width, and height to get the volume. 3. Write the answer in cubic units. Did this summary help you? Yes No

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Word Problem Involving the Volume of a Rectangular Prism

In this lesson we solve word problems involving the volume of a rectangular prism.

Sarah has a chocolate box whose length is 12 cm, height 9 cm, and width 6 cm. Find the volume of the box.

The given box has length = 12 cm; width = 6 cm; height = 9 cm.

The volume of box V = l × w × h = 12 × 6 × 9

= 648 cubic cm

A water tank is 90 m long and 60 m wide. What is the volume of the water in the tank, if the depth of water is 40 m?

The given tank has length = 90 m; width = 60 m; height = 40 m.

The volume of water tank V = l × w × h = 90 × 60 × 40

= 216000 cubic m.

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Word Problems Involving Volume of Cubes and Rectangular Prisms

Here, you will learn how to solve word problems involving the volume of cubes and rectangular prisms.

A step-by-step guide to using a table to write down a two-variable equation

here’s a step-by-step guide to solving word problems involving volume of cubes and rectangular prisms:

• Read the problem carefully: Make sure you understand the information provided in the problem and what is being asked of you.
• Identify the dimensions of the cube or rectangular prism: Look for the measurements of the length, width, and height of the object. Make sure you identify which dimension corresponds to which measurement.
• Calculate the volume: Once you have identified the dimensions of the object, use the formula for finding the volume of a cube or rectangular prism, depending on the shape of the object. The formula for the volume of a cube is \(V = s^3\), where s is the length of one side of the cube. The formula for the volume of a rectangular prism is \(V = lwh\), where l is the length, w is the width, and h is the height of the rectangular prism. Substitute the appropriate values into the formula to calculate the volume.
• Check your units: Make sure that the units of measurement used in the problem are consistent with the units used in the formula for finding the volume. If not, convert the units as necessary.
• Round your answer: Round your answer to the appropriate number of significant figures, as specified in the problem.
• Interpret your answer: Make sure you answer the question that is being asked in the problem. For example, if the problem asks for the volume of a rectangular prism in cubic inches, make sure your answer is expressed in cubic inches.
• Check your work: Double-check your calculations to make sure you have not made any errors.

It’s always a good idea to practice with a variety of problems to become comfortable with these steps.

Word Problems Involving Volume of Cubes and Rectangular Prisms – Example 1

Emma has a rectangular prism box for packing birthday presents that has a volume of 16600 cubic centimeters. The prism has a width of 28 centimeters and a height of 17 centimeters. What is the length of the box? Solution: To find out the length of the present box: Step 1: Multiply the width by height. \(28×17=476\) Step 2: Divide 16600 by 476 to find the length of the box. \(16600÷476=35\) So, the length is 35 cm.

Word Problems Involving Volume of Cubes and Rectangular Prisms – Example 2

Luci bought a handmade rug for her mother’s birthday party. She returned home with a box that was 32 inches long, 24 inches wide, and 9 inches tall. What is the volume of the box? Solution: To find out the volume of the box (V), use the formula for the volume of a rectangular prism. \(V=lwh\). \(32×24×9=6912 in^3\) So, the area of the box is \(6912 in^3\).

by: Effortless Math Team about 2 years ago (category: Articles )

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SOLVING VOLUME PROBLEMS

When we solve a real-world problem involving the volume of a prism, we can  choose to use either of the volume formulas we know.

Example 1 :

A terrarium is shaped like a rectangular prism. The prism is 25  inches long,  13  inches wide, and 16 inches deep. What is the volume of the terrarium ?

From the given information, we can have the following figure. 

Step 2 : 

In the above figure, the base is in the shape of a rectangle with length 25 inches and width 13 inches.  

Therefore, 

Area of the base  =  length x width 

Area of the base  =  25 x 13

Area of the base  =  325 square inches.

Step 3 : 

Volume of the terrarium  =  Volume of rectangular prism 

Volume of the terrarium  =  Base area x Height 

Volume of the terrarium  =  325 x 16

Volume of the terrarium  =  5200 cubic inches

Example 2 :

A rectangular swimming pool is 15 meters long, 10 1/ 2 meters wide,  and 2 1/ 2 meters deep. What is its volume?

In the above figure, the base is in the shape of a rectangle with length 15 meters and width 10 1/2 meters. 

Area of the base  =  15 x 10 1/2

Area of the base  =  15 x 10.5

Area of the base  =  157.5

Area of the base  =  157.5 square inches.

Volume of swimming pool  =  Volume of rectangular prism 

Volume of the  swimming pool   =  Base area x Height 

Volume of the  swimming pool   =  157.5 x 2 1/2

Volume of the  swimming pool   =  157.5 x 2.5

Volume of the swimming pool  =  393.75

Volume of the swimming pool  =  393 75/100

Volume of the swimming pool  =  393 3/4 cubic meters

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Breadcrumbs

Rectangular prisms & cubes

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Calculating volumes

Students calculate the volume or missing side length of rectangular prisms . In the last worksheet, students determine whether shapes are cubes.

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More geometry worksheets

Browse all of our geometry worksheets , from the basic shapes through areas and perimeters, angles, grids and 3D shapes.

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Grade 4 Mathematics Module: Problems Involving the Volume of a Rectangular Prism

This Self-Learning Module (SLM) is prepared so that you, our dear learners, can continue your studies and learn while at home. Activities, questions, directions, exercises, and discussions are carefully stated for you to understand each lesson.

Each SLM is composed of different parts. Each part shall guide you step-by-step as you discover and understand the lesson prepared for you.

Pre-tests are provided to measure your prior knowledge on lessons in each SLM. This will tell you if you need to proceed on completing this module or if you need to ask your facilitator or your teacher’s assistance for better understanding of the lesson. At the end of each module, you need to answer the post-test to self-check your learning. Answer keys are provided for each activity and test. We trust that you will be honest in using these.

Please use this module with care. Do not put unnecessary marks on any part of this SLM. Use a separate sheet of paper in answering the exercises and tests. And read the instructions carefully before performing each task.

Good day to you! From the previous module, you learned how to find the volume of a rectangular prism.

This time you will learn how to solve problems involving the volume of a rectangular prism in real life. Have fun!

After going through this module, you are expected to be able to solve routine and non-routine problems involving the volume of a rectangular prism.

Grade 4 Mathematics Quarter 4 Self-Learning Module: Problems Involving the Volume of a Rectangular Prism

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