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 140 pi, what is the area of the base of the cylinder?

1 Answer
Nov 16, 2017

S=5pi

Explanation:

The volume of a cylinder V is V=Sh, where S is the area of the base and h is the height.
The volume of a cone is V=1/3Sh.

Let S the area of the base in this solid.
The volume of the cone is V_"co"=1/3*S*33=11S and the volume of the cylinder is V_"cy"=S*17=17S

The total volume is V=V_"co"+V_"cy"=11S+17S=28S.
Therefore,
28S=140pi
S=5pi
is the required answer.