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 24 and the height of the cylinder is 4 . If the volume of the solid is 90 pi, what is the area of the base of the cylinder?

1 Answer
Dec 28, 2017

Base Area = 23.56

Explanation:

Combine the equations for the volumes of the cylinder and the cone to find the radius. Then calculate the base area (pir^2).

V_"cone" = 1/3pir^2h
V_"cyl" = pir^2h

V = 90pi = 1/3pir^2h + pir^2h

90 = 1/3r^2xx24 + r^2xx4 = 12r^2
r^2 = 7.5

Because we want r^2 for the area anyway, we do not need to go further.
Base Area = pir^2 = pixx7.5 = 23.56