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?

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Answer 1 · 2017-11-16T01:52:31

$S=5pi$

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.

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 pi140 pi, what is the area of the base of the cylinder?