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 $27$ $27$ and the height of the cylinder is $11$ $11$ . If the volume of the solid is $120 π$ $120 pi$ , what is the area of the base of the cylinder?

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Answer 1 · 2017-05-02T08:32:00

The area is $= 18.8 u^{2}$ $=18.8u^2$

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

Volume of cone is $V_{c o} = \frac{1}{3} \cdot a \cdot h_{c o}$ $V_(co)=1/3*a*h_(co)$

Volume of cylinder is $V_{c y} = a \cdot h_{c y}$ $V_(cy)=a*h_(cy)$

Total volume

$V = V_{c o} + V_{c y}$ $V=V_(co)+V_(cy)$

$V = \frac{1}{3} a h_{c o} + a h_{c y}$ $V=1/3ah_(co)+ah_(cy)$

$120 π = a (\frac{1}{3} \cdot 27 + 11)$ $120pi=a(1/3*27+11)$

$120 π = a \cdot 20$ $120pi=a*20$

$a = \frac{120}{20} π$ $a=120/20pi$

$a = 6 π$ $a=6pi$

$a = 18.8 u^{2}$ $a=18.8u^2$

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 27 2727 and the height of the cylinder is 11 1111 . If the volume of the solid is 120 pi120π120 pi, what is the area of the base of the cylinder?