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 $9$ and the height of the cylinder is $6$ . If the volume of the solid is $130 pi$ , what is the area of the base of the cylinder?

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Answer 1 · 2016-12-15T06:15:57

The answer is $=45.4$

Let area of base $=a$

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

The volume of the cylinder $=a*H$

Total volume $V=1/3ah+aH=a(h/3+H)$

$V=130pi$

height of cone $h=9$

height of cylinder $H=6$

So,

$a(9/3+6)=130pi$

$9a=130pi$

$a=130/9pi=45.4$

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 9 9 and the height of the cylinder is 6 6 . If the volume of the solid is 130 pi130 pi, what is the area of the base of the cylinder?