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 $17$ . If the volume of the solid is $42 pi$ , what is the area of the base of the cylinder?

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Answer 1 · 2016-11-23T16:20:17

Express the volume in function of the area of the base.

If A is the are of the common base:

$V_"cylinder" = A * h = 17A$
$V_"cone" = A * h / 3 = 33 * A / 3 = 11A$

Total volume is $(17A+11A) = 28A = 42pi$ , so the are is:

$A= 42/28 * pi = 3/2*pi$

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 33 33 and the height of the cylinder is 17 17 . If the volume of the solid is 42 pi42 pi, what is the area of the base of the cylinder?