How to Calculate the Volume of a Box

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This article was co-written by Grace Imson, MA. Grace Imson is a math teacher with over 40 years of teaching experience. Grace is currently a math teacher at City University of San Francisco and previously worked in the math department of Saint Louis University. She has taught math at the elementary, middle, high, and college levels. She holds a master’s degree in education from Saint Louis University, majoring in management and supervision in education.

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Whether you want to calculate the volume of a box to send a parcel or to pass an upcoming test, it’s pretty simple. Volume is a value that shows how large an object is in three dimensions, so based on the volume of the box, you will know how much space is in the box. To calculate the volume, you need to take a few simple measurements to get the length, width, and height of the box, and then multiply them together.

Table of Contents

Calculate the volume of the rectangular box

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The volume of a rectangular box is equal to length x width x height . If the box is a rectangle or a cube, you just need to measure the length, width and height, then multiply them to get the volume. This formula is often abbreviated as V = lxwx h.

Example : “If you have a box with a length of 10cm, a width of 4cm, and a height of 5cm, what is the volume of the box?”
V= lxwxh
V= 10cm x 4cm x 5cm
V= 200cm ³
“Height” is also known as “depth”. For example, “The box is 10cm long, 4cm wide, and 5cm deep “.

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Measure the box length. If you look at the box from the top, you will see that the top of the box is like a flat rectangle, the longest side of this shape is the length of the box. You measure this edge and write that value for “length”.

Remember to use one unit of measure for all sides — if you measure one side in centimeters, use this unit for all the other sides.

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Measure the box width. Width is the measure of the side adjacent to the side you just measured the length of. If you look at half of the box, the width and length together make an “L”. You measure and write that value for “width”.

The width is always the shorter side.

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Measure height. This is the last dimension you haven’t measured yet, and it’s the distance from the top to the bottom of the box. You measure and write that value for “height”.

Depending on how you place the box, the “height” or “length” measuring side may be different. However, this is not very important, you just need to measure all 3 different sides.

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Multiply the three sides together. You need to remember the formula to calculate the volume is V = length x width x height , you just need to multiply all 3 sides together to get the volume. Remember to write down the unit of measure so that you don’t forget the meaning of the number you just calculated.

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Add “unit ³ ” after the volume. Volume is a measurement, but if you don’t know the unit, it’s just a meaningless number. To write the correct volume, you need to add the cubic unit . For example, if you measure all sides in centimeters, you need to add “cm ³ ” to the final result. For example:

Example Problem: “If you have a box with a length of 2cm, a width of 1cm, and a height of 4cm, what is the volume of the box?”
V = lxwxh
V = 2cm x 1cm x 4cm
Volume = 8cm ³
Note: The unit of volume is cubic because volume indicates how many cubes you can put in your box. For example, you can put 8 cubes with sides 1cm in the box in the example above.

Calculate the volume of a box of different shapes

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Calculate the volume of the cylinder. The cylinder is in the form of a tube with two round bases. To calculate the volume of a cylinder, you use the formula V= pi xr ² x h. Where pi = 3.14, r is the radius of the base circle, and h is the height.

To calculate the volume of a cone, or pyramid with a rounded bottom, you use the same formula to multiply by 1/3. We have the volume of the cone =1/3(pi xr ² xh)

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Calculate the volume of the pyramid. The pyramid has one base edge and the remaining edges share the same vertex. To calculate the volume of a pyramid, you multiply the area of the base by the height, then multiply by the fraction 1/3. We might like the pyramid = 1/3(base area x height).

Most pyramids have a square or rectangular base. To calculate the area of the base, simply multiply the base length times the width.

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Add volume by parts to calculate the volume of complex shapes. For example, if you need to find the volume of an “L” shaped box, you must measure more than 3 sides. However, if you consider them to be two smaller boxes, you can calculate the volume of each of the smaller boxes, and then add them together to find the volume of the large box. For example, with the “L” shaped box, you can think of the vertical side as a rectangular box and the horizontal bottom edge as a square box.

For more complex cases, there are many ways you can calculate the volume of any shape.

Steps

Calculate the volume of the rectangular box

Calculate the volume of a box of different shapes

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