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 $4$ . If the volume of the solid is $144 pi$ , what is the area of the base of the cylinder?

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Answer 1 · 2016-09-09T14:25:50

Base area of cylinder $=9pi$

As the cone and the cylinder have a same radius, their base area is also the same.

Let base area = A = $pir^2$ .
cone volume $=pir^2xx(h1)/3$ , (h1=36) = $Axx36/3 = 12A$
cylinder volume = $pir^2xxh2$ , (h2=4) = $Axx4=4A$

solid volume = cone volume + cylinder volume
$144pi= 12A+4A = 16A$

$A =(144pi)/16 =9pi$

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 4 4 . If the volume of the solid is 144 pi144 pi, what is the area of the base of the cylinder?