Question

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 `36` and the height of the cylinder is `5`. If the volume of the solid is `48 pi`, what is the area of the base of the cylinder?

Answer 1

`48 pi/17` sq units

Explanation:

For finding the area of the base of the cylinder, its radius needs to be determined.

Given premise is that radius of the base of the cylinder is same as the radius of the cone. Hence let it be = 'r'

Volume of the cylinder would be= `pi r^2h=5pi r^2`

Volume of the cone would be = `1/3 pi r^2 h= 1/3 pi (36)r^2 = 12 pi r^2`

Volume of the whole solid would be `5 pi r^2 + 12 pi r^2= 17 pi r^2`

Thus `17 pi r^2 = 48 pi` which gives `r^2 = 48/17`

Area of the base of the cylinder would be `pi r^2`= `48 pi/ 17` sq units.