Volume of a box

Given the length, the height, and the width, the volume of a box also called rectangular prism can be found by using the following formula in the figure below.

It is not always straightforward to label the height, the width, and the length. It is just a matter of perspective!

Looking at the box below, what I labeled as length could also be called width and vice versa.

And it you rotate the box by 90 degrees, what looks like the length right now will look like the height.

Finally, the volume is expressed in cubit unit. 

Therefore, if the unit you are using is meter, the volume is expressed in cubic meter or meter³

If the unit you are using is ft, the volume is expressed ft³

Enough talking! Let us compute some volume

Some examples showing how to find the volume of a box or rectangular prism.

Example #1:

Find the volume with a length of 5 inches, a height of 2 inches, and a width of 4 inches

V_box = l × w × h

V_box = 5 inches × 4 inches × 2 inches

V_box = 20 inches² × 2 inches

V_box = 40 inches³

Example #2:

An LCD tv was put in a box with a length of 2 feet, a height of 3 feet, and a width of 0.5 foot. What is the volume of the box?

V_box = l × w × h

V_box = 2 × 0.5 × 3

V_box = 1 ft² × 3 ft

V_box = 3 ft³

Example #3:

A swimming pool is shaped like a big box with a length of 10 feet, a height of 8 feet, and a width of 20 foot. What is the volume of the swimming pool?

V_box = l × w × h

V_box = 10 × 20 × 8

V_box = 200 ft² × 8 ft

V_box = 1600 ft³

Example #4:

A packaging box has a length of 9 inches, a height of 5 inches, and a width of 8 inches. What is the volume of the packaging box?

V_box = l × w × h

V_box = 9 × 8 × 5

V_box = 72 in² × 5 in

V_box = 360 in³

Take the quiz below to see how well you can find the volume of a box or rectangular prism.