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 18 and the height of the cylinder is 1 . If the volume of the solid is 84 pi, what is the area of the base of the cylinder?

1 Answer
Jun 27, 2016

12pi

Explanation:

Assume the radius of the cylinder/cone as r, height of cone as h_1, height of cylinder as h_2

Volume of the cone part of solid = (pi*r^2*h_1)/3

Volume of the cylinder part of solid = pi*r^2 * h_2

What we have is:

h_1 = 18,h_2 = 1

(pi*r^2*h_1)/3 + pi*r^2 * h_2 = 84*pi

(pi*r^2*18)/3 + pi*r^2 * 1 = 84*pi

pi*r^2 * 6 + pi*r^2 * 1 = 84*pi

pi*r^2 * 7 = 84*pi

r^2 = 84/7 = 12

Area of the base of the cylinder = pi*r^2 = pi*12 = 12pi