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 `66` and the height of the cylinder is `5`. If the volume of the solid is `35 pi`, what is the area of the base of the cylinder?

Answer 1

Area of cylinder base `color(green)(= pi r^2 ~~ 4.0724` sq units.

Explanation:

Volume of cone = (1/3) pi r^2 h = (1/3) pi r^2 * 66 = 22 pi r^2#

Volume of cylinder = pi r^2 H = pi r^2 * 5#

Volume of the solid `= V = (1/3) pi r^2 h + pi r^2 H 35 pi`

`:. 22 pi r^2 + 5 pi r^2 = 35 pi`

`27 pi r^2 = 35 pi`

Area of cylinder base `color(green)(= pi r^2 = (35 pi)/ 27 ~~ 4.0724` sq units.