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#