As we saw with cylinders, the volume $V$ of a cone depends on the radius $r$ of the base and the height $h$:

$\displaystyle V=\frac13 \pi r^2h$

If we know the radius and height, we can find the volume. If we know the volume and one of the dimensions (either radius or height), we can find the other dimension.

For example, imagine a cone with a volume of $64\pi$ cm³, a height of 3 cm, and an unknown radius $r$. From the volume formula, we know:

$\displaystyle 64 \pi = \frac{1}{3}\pi r^2 \boldcdot 3$

Looking at the structure of the equation, we can see that $r^2 = 64$, so the radius must be 8 cm.

Now imagine a different cone with a volume of $18 \pi$ cm³, a radius of 3 cm, and an unknown height $h$. Using the formula for the volume of the cone, we know:

$\displaystyle 18 \pi = \frac{1}{3} \pi 3^2h$

So, the height must be 6 cm. Can you see why?