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 $42$ and the height of the cylinder is $1$ . If the volume of the solid is $195 pi$ , what is the area of the base of the cylinder?

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Answer 1 · 2016-06-11T14:12:28

Area of the base $= 13 pi$

The volume of the shape consists of two volumes added together:

Vol = vol cone + vol cylinder

Vol = $(pi r^2 H)/3 + pi r^2 h " the radius is the same"$

$195 pi = (cancel42^14 pi r^2)/cancel3 + 1 pi r^2$

$195 pi = 14 pi r^2 + 1 pi r^2 = 15 pi r^2$

$195 pi = 15 pi r^2" (but the area we want is "pi r^2)$

$(195 pi)/15 = (15 pi r^2)/15$

$pi r^2 = 13 pi$

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 42 42 and the height of the cylinder is 1 1 . If the volume of the solid is 195 pi195 pi, what is the area of the base of the cylinder?