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 $33$ and the height of the cylinder is $13$ . If the volume of the solid is $232 pi$ , what is the area of the base of the cylinder?

Question

1193 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-11-15T09:24:53

The area of the base $=9.7pi$

Let the area of the base of cylinder $=a$

Then the area of the base of the cone $=a$

The volume of the cone $=1/3a*h$

where $h$ is the height of the cone

The volume of the cylinder is $=a*H$

where $H$ is the height of the cylinder

The total volume is $=232pi$

then, $232pi=1/3*a*h+a*H$

But $h=33$ and $H=13$

Therefore, $232pi=1/3*a*33+13a=24a$

$a=232pi/24=9.7pi$

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 33 33 and the height of the cylinder is 13 13 . If the volume of the solid is 232 pi232 pi, what is the area of the base of the cylinder?