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 `11`. If the volume of the solid is `140 pi`, what is the area of the base of the cylinder?

Answer 1

The formula for volume of a cone is `1/3A_(base) xx h` while the formula for volume of a cylinder is `A_(base) xx h`. The area of the base is the formula for the area of a circle, so `pi xx r^2`

Explanation:

We are searching for area of base. First though, we must find the radius, r.

`1/3 xx 9 xx (r^2 xx pi) + (r^2 xx pi) xx 11 = 140pi`

`3pir^2 + 11pir^2 = 140pi`

`pi(3r^2 + 11r^2) = 140pi`

`14r^2 = (140pi)/pi`

`r^2 = 10`

`r = sqrt(10)`

`A = r^2 xx pi`

`A = (sqrt(10))^2 xx pi`

`A = 10pi`

The area of the base of the cylinder measures `10pi` square units.

Hopefully this helps!