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 $9$ and the height of the cylinder is $6$ . If the volume of the solid is $140 pi$ , what is the area of the base of the cylinder?

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Answer 1 · 2018-05-11T16:51:08

Area of Base $= (140pi)/9$

Cone Volume = $(1/3)(pi)(r^2)h$ where h = 9
Cylinder Volume = $(pi)(r^2)h$ where h = 6

Note: Area of the Base = B= $(pi)(r^2)$ so we can replace in the formulas as well since Radius is same for both solids.

Total Volume = Cone Volume + Cylinder Volume
$140pi = (1/3)B(9) + B(6)$
$140pi = 3B + 6B = 9B$
$B = (140pi)/9$

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 9 9 and the height of the cylinder is 6 6 . If the volume of the solid is 140 pi140 pi, what is the area of the base of the cylinder?