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 `9` and the height of the cylinder is `6`. If the volume of the solid is `45 pi`, what is the area of the base of the cylinder?

Answer 1

Volume of a cone is given by `V = 1/3pir^2h`

Volume of a cylinder is given by `V = pir^2h`

`1/3pi(r)^2(9) + r^2(6)(pi) = 45pi`

`3r^2pi + 6r^2pi = 45pi`

`9r^2pi = 45pi`

`9r^2 = (45pi)/pi`

`9r^2 = 45`

`r^2 = 5`

`r = sqrt(5)`

The area of a circle is given by `r^2pi`

`(sqrt(5))^2pi`

=`5pi`

The area of the base of the cylinder is `5pi`

Hopefully this helps!