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 $4$ $4$ . If the volume of the solid is $225 π$ $225 pi$ , what is the area of the base of the cylinder?

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Answer 1 · 2017-02-25T16:33:29

The area of the base is $= 47.1 u^{2}$ $=47.1u^2$

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

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

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

$225 π = a (\frac{1}{3} \cdot 33 + 4)$ $225pi=a(1/3*33+4)$

$225 π = a \cdot 15$ $225pi=a*15$

$a = \frac{225}{15} π = 15 π$ $a=225/15pi=15pi$

$a = 47.1$ $a=47.1$

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 3333 and the height of the cylinder is 4 44 . If the volume of the solid is 225 pi225π225 pi, what is the area of the base of the cylinder?