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 $17$ . If the volume of the solid is $18 pi$ , what is the area of the base of the cylinder?

Question

1183 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-12-07T07:04:00

The area of the base $=9/14$

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

The volume of the cone is $=pi/3*a*h_1$

Here, $h_1=33$

The volume of the cylinder is $=pi*a*h_2$

Here, $h_2=17$

Volume of the solid $=18pi$

$18pi=pi/3*a*h_1+pi*a*h_2$

$18=a(33/3+17)=28a$

$a=18/28=9/14$

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 17 17 . If the volume of the solid is 18 pi18 pi, what is the area of the base of the cylinder?