# How To Find The Volume Of Geometric Shapes

## How To Find The Volume Of Three Dimensional Shapes (3D Shapes)

What is the definition of **Volume**? In geometry, the volume of a three dimensional shape (a shape with length and
width and height), is the total interior space of the shape. If you filled the shape
below with water, how much can it hold? The unit of measurement for Volume
of a shape may be any of the following: cubic inches, cubic feet, cubic centimeters,
cubic meters, cubic kilometers, etc.

Let us look at a real example. Picture the diagram below as a plastic box with no
lid i.e. a cubic container where all lengths are the same. Our goal is to fill the
container to the very top with water and, we want known how much water is in the
container. To make the problem easier we assume all sides of this particular container
are 10 inches in length. In other words, the length, width, and height are each
ten inches. The Volume of the container is equal to length times
the width times the height. If the length is 10 inches and the width is 10 inches,
and height are 10 inches then the volume equals 1,000 cubic inches (10 inches × 10 inches
× 10 inches = (10 inches)^{3} = 1,000 cubic inches = 1,000 inches^{3} = 1,000
in^{3}).

When we say cubic inches, picture solid blocks that are one inch in length, width, and height; we could stack 1,000 of these blocks in the 10 by 10 by 10 inch container talked about above.

**Volume Formula**

Formula = Side × Side × Side =

Formula = S × S × S =

Formula = S^{3}