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 $15$ $15$ and the height of the cylinder is $4$ $4$ . 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 · 2017-01-14T13:49:48

The area is $= 2 π$ $=2pi$

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

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

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

$V = \frac{1}{3} \cdot a \cdot h_{c o} + a \cdot h (c y) = 18 π$ $V=1/3*a*h_(co)+a*h(cy)=18pi$

So,

$\frac{1}{3} \cdot a \cdot 15 + a \cdot 4 = 18 π$ $1/3*a*15+a*4=18pi$

$9 a = 18 π$ $9a=18pi$

$a = 2 π$ $a=2pi$

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 15 1515 and the height of the cylinder is 4 44 . If the volume of the solid is 18 pi18π18 pi, what is the area of the base of the cylinder?