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 $27$ 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 · 2017-02-03T14:19:19

The area is $=(21/8pi) u^2$

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

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

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

$42pi=a(1/3*27+7)$

$42pi=a*16$

$a=42/16pi=21/8pi$

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 27 27 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?