Question

A solid consists of a cone on top of a cylinder with a radius equal to the cone. The height of the cone is `3` and the height of the cylinder is `5`. If the volume of the solid is `25 pi`, what is the area of the base of cylinder?

Answer 1

The answer is 13.09 square units.

Explanation:

Let V, be the volume of the solid figure
V1, be the volume of the cone
V2, be the volume of the cylinder
h1, be the height of the cone
h2, be the height of the cylinder

therfore

`V= V1 + V2`

`V= [(B1h1/3) + B2h2]`

since the radius of the cone is equal to radius of the cylinder
then B1=B2=B

`V= [(Bh1/3) + Bh2]`
by factoring
`B= (V)/[(h1/3) + h2)`

`B= (25pi)/[(3/3) + 5)`

`B= 13.09 square units`