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 `27` and the height of the cylinder is `11`. If the volume of the solid is `190 pi`, what is the area of the base of the cylinder?

Answer 1

Area of base = `pir^2 = 9.5pi`

Explanation:

Start by writing down the formulae for the volumes of the two shapes: They have the same radius, but different heights.
Cone: `V = 1/3 pi r^2h" Cylinder: "V = pi r^2H`

`V = 1/3 pi r^2h + pi r^2H = 190pi`

Factorise: `pi r^2(1/3 h + H) = 190pi`

Substitute: `pi r^2(1/3xx 27 + 11) = 190pi`

`pi r^2(9+11) = 190pi`

`20pir^2 = 190pi`

The area of the base of the cylinder is `pir^2`, so solve for this

`pir^2 = (190pi)/20`

Area of base = `pir^2 = 9.5pi`