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 $33$ and the height of the cylinder is $5$ . If the volume of the solid is $12 pi$ , what is the area of the base of the cylinder?

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Answer 1 · 2018-01-08T07:31:33

Area of base of the cylinder $A_b = (3pi)/4 = color (red)(2.3562)$

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Volume of solid $V_s$ = vol. of cylinder + vol. of cone

Given $V_s = 12pi, h_(cyl) = 5, h_(co) = 33$

$V_s = 12pi = (pi r^2 h_(cyl) + (1/3) pi r^2 h_(co))$

$12pi = pi r^2(5 + (1/3)33) = 16 pi r^2$

$r^2 = (12 pi) / (16 pi) = (3/4)$

$Area of base A_b = pi r^2 = pi * (3/4) = 2.3562$

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 5 5 . If the volume of the solid is 12 pi12 pi, what is the area of the base of the cylinder?