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 $18$ and the height of the cylinder is $36$ . If the volume of the solid is $420 pi$ , what is the area of the base of the cylinder?

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Answer 1 · 2018-07-30T02:22:16

$color(green)("radius of the cone " = r = sqrt 10, " units"$

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$"Given " h_1 = 18, h_2 = 36, V = 420 pi$

$"Volume of the solid " = V = V_(cone) + V_(cyl)$

$V_(cone) = 1/3 pi r^2 h = 1/3 pi r^2 18 = 6 pi r^2$

$V_(cyl) = pi r^2 h = pi r^2 36 = 36 pi r^2$

$V = 6 pi r^2 + 36 pi r^2 = 420 pi$

$42 pi r^2 = 420 pi$

$r^2 = cancel(420 pi)^color(red)(10) / cancel(42 pi) = 10$

$color(green)("radius of the cone " = r = sqrt 10, " units"$

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 18 18 and the height of the cylinder is 36 36 . If the volume of the solid is 420 pi420 pi, what is the area of the base of the cylinder?