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 $33$ and the height of the cylinder is $5$ . If the volume of the solid is $24 pi$ , what is the area of the base of the cylinder?

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Answer 1 · 2018-06-28T20:37:48

${3\pi}/2$

Let $r$ be the radius of base of cone of height 33 & cylinder of height 5 then the volume of composite solid

$24\pi=\text{volume of cone of height 33 & radius r}+\text{volume of cylinder of height 5 & radius r}$

$24\pi=1/3\pir^2\cdot 33+\pir^2\cdot 5$

$24\pi=16\pi r^2$

$\pir^2={24\pi}/16$

$\pir^2={3\pi}/2$

$\therefore \text{area of base of the cylinder}={3\pi}/2$

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 33 33 and the height of the cylinder is 5 5 . If the volume of the solid is 24 pi24 pi, what is the area of the base of the cylinder?