A solid consists of a cone on top of a cylinder with a radius equal to the cone. The height of the cone is $3$ and the height of the cylinder is $12$ . If the volume of the solid is $24 pi$ , what is the area of the base of cylinder?

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Answer 1 · 2017-02-04T06:47:46

The answer is $=24/13pi$

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

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

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

$24pi=a(1/3*3+12)$

$24pi=a*13$

$a=24/13pi$

A solid consists of a cone on top of a cylinder with a radius equal to the cone. The height of the cone is 3 3 and the height of the cylinder is 12 12 . If the volume of the solid is 24 pi24 pi, what is the area of the base of cylinder?