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 $36$ and the height of the cylinder is $8$ . If the volume of the solid is $48 pi$ , what is the area of the base of the cylinder?

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Answer 1 · 2017-01-08T22:15:47

$Area_(base)=12/5pi$

You know that:

$Volume_(solid)=Volume_(co)+Volume_(cy)$

and that

$Volume_(co)=1/3Area_(base)*36$

$Volume_(cy)=Area_(base)*8$

Then

$1/cancel3Area_(base)*cancel36^12+Area_(base)*8=48pi$

that's

$20Area_(base)=48pi$

$Area_(base)=cancel48^12/cancel20^5pi$

$Area_(base)=12/5pi$

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 36 36 and the height of the cylinder is 8 8 . If the volume of the solid is 48 pi48 pi, what is the area of the base of the cylinder?