# A solid consists of a cone on top of a cylinder with a radius equal to that of the cone. The height of the cone is #60 # and the height of the cylinder is #15 #. If the volume of the solid is #7 pi#, what is the area of the base of the cylinder?

##### 1 Answer

The area of the base of the cylinder is

#### Explanation:

The volume of the solid is found by adding the volume of the cylinder to the volume of the cone. The volume of a cylinder is given by

This can be transformed by the converse of the Distributive Property to become:

Which then becomes:

Since we are looking for the area of the base, which is a circle, we need to isolate the part of the formula which gives that area. The area of a circle is given by

Therefore, the area of the base of the cylinder is given by the formula:

Substitute the values you know for

Since the volume in the problem is left in terms of