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 $17$ $17$ . If the volume of the solid is $18 π$ $18 pi$ , what is the area of the base of the cylinder?

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Answer 1 · 2016-12-07T07:04:00

The area of the base $= \frac{9}{14}$ $=9/14$

Let the area of the base of the cylinder be $= a$ $=a$

The volume of the cone is $= \frac{π}{3} \cdot a \cdot h_{1}$ $=pi/3*a*h_1$

Here, $h_{1} = 33$ $h_1=33$

The volume of the cylinder is $= π \cdot a \cdot h_{2}$ $=pi*a*h_2$

Here, $h_{2} = 17$ $h_2=17$

Volume of the solid $= 18 π$ $=18pi$

$18 π = \frac{π}{3} \cdot a \cdot h_{1} + π \cdot a \cdot h_{2}$ $18pi=pi/3*a*h_1+pi*a*h_2$

$18 = a (\frac{33}{3} + 17) = 28 a$ $18=a(33/3+17)=28a$

$a = \frac{18}{28} = \frac{9}{14}$ $a=18/28=9/14$

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 3333 and the height of the cylinder is 1717 . If the volume of the solid is 18π18 pi, what is the area of the base of the cylinder?