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 `66` and the height of the cylinder is `5`. If the volume of the solid is `45 pi`, what is the area of the base of the cylinder?

Answer 1

`5/3 pi`

Explanation:

Let the 'radius' be r unit.
We know the volume of a cone = `1/3 pi r^2 h_1` cu. units [ `h_1` is height which = 66.]

& volume of a cylinder = `pi r^2 h_2` cu. units. [`h_2` is height which equals to 5]

As per questions, `1/3 pi r^2 h_1 + pi r^2 h_2 = 45 pi`

`rArr pi r^2[1/3* 66 + 5] = 45 pi`

`rArr r^2*27 = 45`

`rArr r^2 = 45/27`

Now area of the base of the cylinder = `pi*r^2 = pi*45/27= 5/3 pi`