What Is Volume, in Geometry?

Volume is the space inside a three-dimensional shape

Volume is how much three-dimensional space a shape takes up. In geometry, we're usually looking for a measurement when we're talking about volume. Volume is a three-dimensional measurement, so we always report it in $\text{[units]}^3$ ("units cubed").

For example, the box below has a $\text{width}$, a $\text{length}$ and a $\text{height}$. To find the volume, we multiply $\text{width}\times\text{height}\times\text{height}$. If we use the following measurements, we get: $$\text{length} = 4\text{in} \\ \text{width} = 4\text{in} \\ \text{height} = 10\text{in} \\ \\\ \\ 4\text{in} \times 4\text{in} \times 10\text{in} = 160\text{in}^3.$$

There are formulas you can use to find the volume of certain shapes. Find common ones here.