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 `33` and the height of the cylinder is `17`. If the volume of the solid is `18 pi`, what is the area of the base of the cylinder?

Answer 1

The area of the base `=9/14`

Explanation:

Let the area of the base of the cylinder be `=a`

The volume of the cone is `=pi/3*a*h_1`

Here, `h_1=33`

The volume of the cylinder is `=pi*a*h_2`

Here, `h_2=17`

Volume of the solid `=18pi`

`18pi=pi/3*a*h_1+pi*a*h_2`

`18=a(33/3+17)=28a`

`a=18/28=9/14`