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 pi140π, what is the area of the base of the cylinder?

1 Answer
Mr. Hsia
May 11, 2018

Area of Base = (140pi)/9=140π9

Explanation:

Cone Volume = (1/3)(pi)(r^2)h(13)(π)(r2)h where h = 9
Cylinder Volume = (pi)(r^2)h(π)(r2)h where h = 6

Note: Area of the Base = B= (pi)(r^2)(π)(r2) 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)140π=(13)B(9)+B(6)
140pi = 3B + 6B = 9B140π=3B+6B=9B
B = (140pi)/9B=140π9

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