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Plus practice problems for finding a rectangular prism’s volume
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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 .
Steps
Section 2 of 7:
Finding the Volume of a Rectangular Prism (With Cube Units)
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If you’re only given cube units, start by identifying the side length of a single cube. The space inside of a rectangular prism is made up of cube units, meaning that a rectangular prism can be visualized as a 3D shape with many smaller cubes fitting inside it—almost like a 3-dimensional grid inside the prism. [5] X Research source If you’ve been given a rectangular prism problem where the prism is divided up into cubes and you’re only given the side length of each cube , follow this set of steps.
- 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 .
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Decide how many cubes make up the bottom layer of the prism. Look at the bottom layer of the rectangular prism. Count how many cubes are included in the long side of the prism. Then, count how many cubes are included on the short side.
- 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.
-
Determine the length and width of the prism’s bottom layer. Now that you know how many cubes make up the long and short sides of the prism’s bottom layer, you can determine the prism’s total length and width.
- To find the length
, multiply the side length of your cubes by the number of cubes on the long
side of the bottom layer.
- 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 .
- To find the width
, multiply the side length of your cubes by the number of cubes on the short
side of the bottom layer.
- 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 .
- To find the length
, multiply the side length of your cubes by the number of cubes on the long
side of the bottom layer.
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Calculate the volume of the rectangular prism’s bottom layer. You now have the length and width of the bottom layer of your prism. You also know that layer’s height, which is equal to the side length of a single cube. To find the volume of that layer (just that layer—not the entire prism), multiply length by width by height. [6] X Research source
- 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
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Add together the volume of each layer to find the prism’s total volume. You now know the volume of the bottom layer of the prism. The great news is that every layer has the same volume—so we’re almost there! Count the total number of layers in your prism, then add together your volume answer from the previous amount of steps that amount of times. [7] X Research source
- 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
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Make sure to include cubic units when writing down your final answer. Determine the original units of the rectangular prism (e.g, inches, centimeters, feet, etc.). Write the final volume in cubic units matching your original units. [8] X Research source
- 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 .
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Community Q&A
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QuestionIf l=45, w=15, h=x, how do I find the volume?DonaganTop AnswererYou have to know the height. Otherwise, you'd have to say the volume is 675x cubic units.
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QuestionCan you give me another example? I still don't get it.Community AnswerRemember that length x width x height. A rectangular prism that is five inches high, ten inches long, and two inches deep will have a volume of 100 square in. 5x10x2=100.
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QuestionHow can I calculate the dimension when I know the volume?Community AnswerThe rectangle's area, times the prism's height vertical to the rectangle, gives the volume; various combinations of dimensions give the same volume, so if you know the volume, and want the dimensions, you will find many sets of dimensions. For example volume 24 could give the length, width, and height of 2, 2, and 6; or 2, 3, 4; or 1, 1, 24; and so on.
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Tips
- 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 sourceThanks
- 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
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References
- ↑ 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://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://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://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://www.ohlone.edu/mathmods/mathmod8
- ↑ 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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Article Summary
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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.
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