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 `42` and the height of the cylinder is `6`. If the volume of the solid is `60 pi`, what is the area of the base of the cylinder?

Answer 1

Area of base of cylinder is `3pi`

Explanation:

As the two have same radius, let it be `r`.

As height of cylinder is `6`, its volume is `6pir^2`

and as height of cone is `42`, its volume is `1/3xxpir^2xx42=14pir^2`

and volume of solid is `6pir^2+14pir^2=20pir^2`

But as volume is `60pi`, we have `20pir^2=60pi`

and hence `r^2=(60pi)/(20pi)=3`

and area of base of cylinder is `pir^2=pixx3=3pi`