# 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 #9 # and the height of the cylinder is #12 #. If the volume of the solid is #15 pi#, what is the area of the base of the cylinder?

##### 1 Answer

Aug 16, 2017

#### Explanation:

The base of a cylinder is a circle. The area of a circle is

The volume of a cone is

#V_"cone" = 1/3pir^2*9 = 3pir^2#

The volume of a cylinder is

#V_"cylinder" = pir^2*12 = 12pir^2#

We also know that the volume of the cone plus that of the cylinder is equal to

#V_"cone" + V_"cylinder" = 15pi#

#3pir^2 + 12pir^2 = 15pi#

#15pir^2 = 15pi#

Dividing by

#r^2 = 1#

#r=1#

So, the area of the base of the cylinder is

#pir^2 = pi* 1^2 = pi#