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 `12`. If the volume of the solid is `25 pi`, what is the area of the base of cylinder?

Answer 1

`25/13 pi` sq unit

Explanation:

We know the vol of a cone is `1/3 pi r^2 h1` cu unit where h1 is height of cone and r is radius of cone. we also know the vol of cyl is `pi r^2 h2` cu unit where h2 is height of cyl and radius is same as cone
So as per question, `1/3 pi r^2 h1 + pi r^2 h2 = 25 pi`
or, `pi r^2(1/3 h1+h2) = 25 pi`
or, `r^2(1/3 * 3 + 12) = 25`
or, `r^2 = 25/13`

Now the area of base of cyl is `pi r^2` = `25/13 pi` sq unit