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 $42$ and the height of the cylinder is $1$ . If the volume of the solid is $480 pi$ , what is the area of the base of the cylinder?

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Answer 1 · 2017-02-20T12:36:41

The area of the base $=32pi=100.5u^2$

Let $a=$ area of the base

Volume of cone is $V_(co)=1/3*a*h_(co)$

Volume of cylinder is $V_(cy)=a*h_(cy)$

Total volume

$V=V_(co)+V_(cy)$

$V=1/3ah_(co)+ah_(cy)$

$480pi=a(1/3*42+1)$

$480pi=a*15$

$a=480/15pi=32pi$

$a=100.5$

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 42 42 and the height of the cylinder is 1 1 . If the volume of the solid is 480 pi480 pi, what is the area of the base of the cylinder?