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 $7$ . If the volume of the solid is $42 pi$ , what is the area of the base of the cylinder?

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Answer 1 · 2017-01-01T09:11:57

The area of the base $=4.2pi=13.2 (unit)^2$

Volume of the cone is $=1/3*a*h$

Where,

$a=$ area of the base

$h=$ height of the cone $=9$

Volume of the cylinder is $=a*H$

where

$H=$ height of the cylinder $=7$

Total volume

$V=1/3*a*h+a*H=42pi$

Therefore,

$a(h/3+H)=42pi$

$a(9/3+7)=42pi$

$10a=42pi$

$a=42/10pi=4.2pi=13.2 (unit)^2$

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 7 7 . If the volume of the solid is 42 pi42 pi, what is the area of the base of the cylinder?