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 $36$ and the height of the cylinder is $4$ . If the volume of the solid is $126 pi$ , what is the area of the base of the cylinder?

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Answer 1 · 2018-06-10T05:36:05

$color(violet)("Area of base of cylinder " = pi r^2 = (126/16) pi = (63/8) pi$

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$"Volume of the solid " V = pir^2 h_1 + (1/3) pi r^2 h_2 = 126 pi$

$pi r^2 (4 + 36/3) = 126 pi$

$color(violet)("Area of base of cylinder " = pi r^2 = (126/16) pi = (63/8) pi$

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 36 36 and the height of the cylinder is 4 4 . If the volume of the solid is 126 pi126 pi, what is the area of the base of the cylinder?