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 21 and the height of the cylinder is 7 . If the volume of the solid is 42 pi, what is the area of the base of the cylinder?

1 Answer
Jun 27, 2016

3pi

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 = 21,h_2 = 7

(pi*r^2*h_1)/3 + pi*r^2 * h_2 = 42*pi

(pi*r^2*21)/3 + pi*r^2 * 7 = 42*pi

pi*r^2 * 7 + pi*r^2 * 7 = 42*pi

pi*r^2 * 14 = 42*pi

r^2 = 42/14 = 3

Area of the base of the cylinder = pi*r^2 = pi*3 = 3pi