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 `4`. If the volume of the solid is `205 pi`, what is the area of the base of the cylinder?

Answer 1

41\3 `pi`

Explanation:

volume of cylinder= `pir^2h` [h=4]
volume of cone= 1\3`pir^2h` [h=33]
volume of solid=205 `pi`
volume of cone +volume of cylinder=volume of solid
1\3 `pir^2`33 + `pir^2` 4 = 205 `pi`
`pir^2`[11+4] =205 `pi`
`r^2`=205\15
`r^2`=41\3

base of cylinder = circle
area of base of cylinder = `pir^2`
= 41\3 `pi`