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 $144 π$ $144 pi$ , what is the area of the base of the cylinder?

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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 $144 π$ $144 pi$ , 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 $= 9 π$ $=9pi$

Explanation:

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

Let base area = A = $π r^{2}$ $pir^2$ .
cone volume $= π r^{2} \times \frac{h 1}{3}$ $=pir^2xx(h1)/3$ , (h1=36) = $A \times \frac{36}{3} = 12 A$ $Axx36/3 = 12A$
cylinder volume = $π r^{2} \times h 2$ $pir^2xxh2$ , (h2=4) = $A \times 4 = 4 A$ $Axx4=4A$

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

$A = \frac{144 π}{16} = 9 π$ $A =(144pi)/16 =9pi$

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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 $144 π$ $144 pi$ , what is the area of the base of the cylinder?

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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 3636 and the height of the cylinder is 44 . If the volume of the solid is 144π144 pi, what is the area of the base of the cylinder?

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Explanation:

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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 $144 π$ $144 pi$ , what is the area of the base of the cylinder?