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How to Find the Volume of a Box

Instructor: Kimberly Osborn
Volume is simply the amount of space that a substance (or object) takes up in a container. In this lesson, you will specifically explore the equation and application for the volume of a box.

Introduction - How much water do I need to fill my new pool?

A few years back, I moved into a new home with a big backyard and an empty swimming pool in the shape of a box. After having the pool cleaned and resurfaced, I was stuck with the dilemma of trying to figure out how much water I needed to fill it. This is where our lesson topic comes into play.

Now, before I begin explaining the definition and equation for the volume of my swimming pool, let's first look at a diagram and see how we would label this diagram to organize our thoughts.

Below you will see a box (or in more formal language, rectangular prism) with the following sides labeled, l, w, and h. Each of these labels correspond with the box's:

  • Length (l)
  • Width (w)
  • Height (h)

Volume of a Box Diagram

However, the length, width, and height of the box are all based on the perspective of how you are looking at the box. When looking at any box, I would recommend picking one corner (I prefer the right bottom corner as shown in the above image) and labeling the three sides that shoot out for that corner.

  • The length follows the horizontal line on the front of your box.
  • The height follows the vertical line on the front of your box.
  • And the width follows the line from the front to the back of the box.

Definition and Equation

Looking back at the example given in the introduction of this lesson, we were tasked with finding the amount of water needed to fill my box shaped swimming pool. This is the classic definition of volume.

Volume is simply the amount of space that a substance (or object) takes up in a container.

In the case of my swimming pool, the water is our substance and the pool itself is our container.

To find the volume (typically noted with a capital V) all we need to do is multiply the length by the width and the height.

The equation for the volume of a box is then:

Volume Equation

Special Case:

When working with a cube (all sides are the same length), your length, width, and height will all be the same. Therefore, the equation for the volume of a cube will be:

V = side x side x side (or side^3)

Units

We know that every time we are working with measurements, we must have units. For example, the units for area of a rectangle is units^2, or square units. These could be inches^2, feet^2, yards^2, etc.

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