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 #12 # and the height of the cylinder is #16 #. If the volume of the solid is #75 pi#, what is the area of the base of the cylinder?

1 Answer
Nov 20, 2016

# (15 pi)/4#

Explanation:

If 'r' is the radius of the cone, its volume would be #1/3 pi r^2 h= 1/3 pi r^2 *12=4 pi r^2 #

Since 'r' is also the radius of the cylinder, its volume would be # pi r^2 h= 16pir^2#

Total area of the solid is thus #4pi r^2 +16 pi r^2 = 20 pi r^2#

Thus # 20 pi r^2 = 75 pi#

#r^2=75 /20=15/4#

Area of the base of the cylinder would be # pi r^2= (15 pi)/4#