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 `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?

Answer 1

`(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`