# 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 #66 # and the height of the cylinder is #5 #. If the volume of the solid is #64 pi#, what is the area of the base of the cylinder?

##### 2 Answers

#### Explanation:

The volume of the cone is given by:

Since the height of the cone is 66, then

So,

The volume of a cylinder is given by:

Since the height of the cylinder is 5, then

So,

The total volume of the solid is

Therefore,

Since r is the radius, it must be have the restriction:

Therefore,

To find the base of the cylinder, we need to know that the base is a circle. The area of a circle is given by

The area of the base of the cylinder is:

#### Explanation:

The area of the base we need to find is:

The volume of the cylinder is:

where

The volume of the cone is

where

The volume of the solid is the sum of those two volumes:

Factoring

And that is the area of the base: