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 `15` and the height of the cylinder is `12`. If the volume of the solid is `18 pi`, what is the area of the base of the cylinder?

Answer 1

Area of the base of cylinder is `3.33` sq.unit.

Explanation:

Let the base radius of cylinder and cone be `r` unit,

Height of cylinder and cone be `h_1=12 and h_2=15` unit

Total volume of composite solid is `18 pi` cubic unit.

Total volume of composite solid is

`V= pi*r^2*h_1+1/3*r^2*h_2` or

`pi*r^2*12+1/3*r^2*15 = 18 pi` or

`pi*r^2(12+5) = 18 pi` or

`pi*r^2 = (18 pi) /17 ~~ 3.33` sq.unit

Area of the base of cylinder is `A=pi*r^2~~ 3.33`sq.unit [Ans]