In an earlier lesson we learned that the volume of a cylinder with radius and height is

We say that the volume depends on the radius and height, and if we know the radius and height, we can find the volume. It is also true that if we know the volume and one dimension (either radius or height), we can find the other dimension.

For example, imagine a cylinder that has a volume of cm³ and a radius of 5 cm, but the height is unknown. From the volume formula we know that

must be true. Looking at the structure of the equation, we can see that . That means that the height has to be 20 cm, since .

Now imagine another cylinder that also has a volume of cm³ with an unknown radius and a height of 5 cm. Then we know that

must be true. Looking at the structure of this equation, we can see that . So the radius must be 10 cm.