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 $320 pi$ , what is the area of the base of the cylinder?

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Answer 1 · 2016-07-16T02:36:58

${64 pi}/3$

We use the formulas $V = 1/3 pi r^2 h$ and $V = pi r^2 h$ for the volumes of a cone and a cylinder, respectively. This gives us

$1/3 pi r^2 42 + pi r^2 1 = 320 pi$

or

$15 pi r^2= 320 pi$

So,

$r^2 = {320}/15 = 64/3$

and the area of the base of the cylinder is given by $pi r^2$

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 320 pi320 pi, what is the area of the base of the cylinder?