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 `39` and the height of the cylinder is `17`. If the volume of the solid is `120 pi`, what is the area of the base of the cylinder?

Answer 1

`pir^2 = 40pi`

Explanation:

This question is surprisingly simple, despite what look like awkward numbers.

`"Vol cone" = 1/3pir^2h` and `"Vol cylinder" = pir^2H`

Total volume = `1/3pir^2h + pir^2H = 120pi`

`1/3pir^2 39 + pir^2 17 = 120pirArr` `1/cancel3pir^2cancel39^13 + pir^2 17 = 120pi`

`13pir^2 + 17 pir^2 = 120pi`

`30 pir^2 = 120pi" divide both sides by 30"`

`pir^2 = 40pi`

Nothing more is needed, because the area of the circular base is given by `pi r^2`.