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 140 pi140π, what is the area of the base of the cylinder?

1 Answer
Nov 16, 2017

S=5piS=5π

Explanation:

The volume of a cylinder VV is V=ShV=Sh, where SS is the area of the base and hh is the height.
The volume of a cone is V=1/3ShV=13Sh.

Let SS the area of the base in this solid.
The volume of the cone is V_"co"=1/3*S*33=11SVco=13S33=11S and the volume of the cylinder is V_"cy"=S*17=17SVcy=S17=17S

The total volume is V=V_"co"+V_"cy"=11S+17S=28SV=Vco+Vcy=11S+17S=28S.
Therefore,
28S=140pi28S=140π
S=5piS=5π
is the required answer.