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1Calculating the Volume of Rectangular Boxes

2Calculating Different Shaped Boxes

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**Co-authored by**Grace Imson, MA

Last Updated: April 12, 2024Fact Checked

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Whether you need to mail a package or pass you next test, finding the volume of a box is easy. Volume is the measure of how big an object is in three dimensions, so the volume of a box measure how much room there is inside of the box. To find it, you need to make a few simple measurements of length, width, and height, and then multiply them.

Method 1

Method 1 of 2:

### Calculating the Volume of Rectangular Boxes

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1

**Understand the volume of a rectangle equals it's**If your box is a rectangular prism or a cube, the only information you need is the box's length, width, and height. You can then multiply them together to get volume. This formula is often abbreviated as*length*x*width*x*height.***V = l x w x h.**^{[1]}*Sample Question:*"If I have a box with a length of 10cm, width of 4cm, and height of 5cm, what is the volume of the box?"- V = l x w x h
- V = 10cm x 4cm x 5cm
- V = 200cm
^{3} - "Height" may be replaced with "depth." For example, "The box has a length of 10cm, width of 4cm, and is 5cm
*deep.*"^{[2]}

2

**Measure the length of a box.**If your are looking down at your box, the top appears to be a flat rectangle/The length the longest side of this rectangle. Write this number down as "length."^{[3]}- Make sure you use the same measurement for each side -- if you measure one side in inches, you need to measure them all in inches.

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3

**Measure the width of the box next to the length.**The width of the box is the other edge next to the length. If you are looking one side of the box, the width is the side the forms an "L" with the length. Write down this measurement as "width."^{[4]}- The width is always the shorter side.

4

**Measure the height of the box.**This is the last side you have not measured, and is the distance from the top of the box to the ground. Write this measurement down as "height."^{[5]}- Depending on how the box is laying, which side you call "height" or "length" might be different. However, it doesn't matter what side you call the length, just that you measure 3 different sides.

5

**Multiply the three sides together.**Remember, the equation for volume is**V = length x width x height**, so simply multiply all three sides together to get your volume. Be sure to include the units you used to measure with as well, so you don't forget what your numbers mean.^{[6]}EXPERT TIP

Grace Imson, MA

Math Instructor, City College of San Francisco

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.

Grace Imson, MA

Math Instructor, City College of San Francisco**Make sure all of the units are the same before multiplying.**Tricky math problems will give a different unit of measurement for the length, width, and height of a box. You cannot multiply the dimensions to find the volume until all the dimensions are in the same unit.6

**Add the "units**Volume is a measurement, but if you don't know what the measuring system your number will be meaningless. The correct way write out volume is with your type of measurement^{3}" to your volume.*cubed*. For example, if I measured all the sides in inches, my final answer would be in "inches^{3}." For example.^{[7]}*Sample Question:*"If I have a box with a length of 2 feet, width of 1 foot, and height of 4 feet what is the volume of the box?"- V = l x w x h
- V = 2ft x 1ft x 4ft
- Volume = 8ft
^{3} *Advanced Note:'*This is because volume tell you how many small cubes you could fit in the box. In the previous example, this means we could fit eight separate 1 foot cubes in our box.

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Method 2

Method 2 of 2:

### Calculating Different Shaped Boxes

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**Find the volume of cylinders.**Cylinders are tubes, where the top and bottom are circles. To find volume of a cylinder, use the equation V = pi x r^{2}x h. Where pi = 3.14, r is the radius of the top circle, and h is the height.^{[8]}- To find the volume of a cone, or pyramid with a circle for the bottom, use the same equation time 1/3. So, Volume of a Cone = 1/3(pi x r
^{2}x h)

- To find the volume of a cone, or pyramid with a circle for the bottom, use the same equation time 1/3. So, Volume of a Cone = 1/3(pi x r
2

**Find the volume of a pyramid.**Pyramids have one side, or base, and all of the other sides comes to a point. To find volume, multiply the area of the base by the height, and then multiply that by the fraction 1/3. Thus, Volume of a Pyramid = 1/3(base x height).^{[9]}- Most pyramids have square or rectangular bases. The area of a base is found by multiplying the length of the base by the width.

EXPERT TIP

Joseph Meyer

Math Teacher

Joseph Meyer is a High School Math Teacher based in Pittsburgh, Pennsylvania. He is an educator at City Charter High School, where he has been teaching for over 7 years. Joseph is also the founder of Sandbox Math, an online learning community dedicated to helping students succeed in Algebra. His site is set apart by its focus on fostering genuine comprehension through step-by-step understanding (instead of just getting the correct final answer), enabling learners to identify and overcome misunderstandings and confidently take on any test they face. He received his MA in Physics from Case Western Reserve University and his BA in Physics from Baldwin Wallace University.

Joseph Meyer

Math Teacher**To find a pyramid's volume, use the formula (1/3) Base Area Height.**Measure a pyramid's height from its tip to the base's center. Next, find the base area using the correct formula for the base shape, whether a triangle, square, or rectangle. Finally, input these values into the formula to calculate volume.3

**Add the volume of the parts together to find the volume of complicated shapes.**For example, if I need to find the volume of an "L" shaped box, there are more than three sides to measure. If you view the box as two smaller boxes, however, you can find the volume of each smaller box and add them together to get the final volume. With our "L" shaped box, for example, we can view the vertical line as a rectangular box and the bottom horizontal line as a square box.^{[10]}- Thought it becomes complicated, there are many ways to find the volume for any shape.

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### Calculator, Practice Problems, and Answers

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## Community Q&A

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Question

How do I tell how many bottles I can put on a tray?

Donagan

Top Answerer

Assuming identical, cylindrical bottles and a square or rectangular tray: Divide the diameter of a bottle into the length of the tray. That's how many bottles you can fit in one direction. Divide the diameter into the width of the tray. That's how many bottles you can fit in the other direction. Multiply the two numbers together to get the total number of bottles that will fit.

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Is it possible to find the volume of a rectangular prism without the depth?

Donagan

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No. The volume is calculated by multiplying the depth (height) by the area of the base.

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How do I convert cubic centimeters into liters?

Donagan

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There are 1,000 cubic centimeters in one liter. To convert cubic centimeters to liters, divide the number of cubic centimeters by 1,000.

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## References

- ↑ https://www.khanacademy.org/math/basic-geo/basic-geo-volume-sa/volume-rect-prism/a/volume-of-rectangular-prisms-review
- ↑ http://thinkmath.edc.org/resource/measurement-length-width-height-depth
- ↑ https://www.omnicalculator.com/math/volume
- ↑ https://www.omnicalculator.com/math/volume
- ↑ https://www.omnicalculator.com/math/volume
- ↑ https://sciencing.com/calculate-area-perimeter-volume-8465825.html
- ↑ https://www.mathopenref.com/cubevolume.html
- ↑ https://www.mathopenref.com/cylindervolume.html
- ↑ https://www.mathopenref.com/pyramidvolume.html

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## About This Article

Co-authored by:

Grace Imson, MA

Math Instructor, City College of San Francisco

This article was co-authored by Grace Imson, MA. 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. This article has been viewed 613,543 times.

12 votes - 60%

Co-authors: 19

Updated: April 12, 2024

Views:613,543

Categories: Volume

Article SummaryX

To calculate the volume of a rectangular box, first measure its length, width, and height. Be sure to use the same units, like inches or centimeters, for all 3 measurements! Then, simply multiply the 3 measurements together using the formula Volume = Length × Width × Height. Finally, add the units cubed. For more on calculating the volume of a box, including a box that’s not rectangular, read on!

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