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 $15$ and the height of the cylinder is $12$ . If the volume of the solid is $18 pi$ , what is the area of the base of the cylinder?

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Answer 1 · 2018-06-12T12:35:36

Area of the base of cylinder is $3.33$ sq.unit.

Let the base radius of cylinder and cone be $r$ unit,

Height of cylinder and cone be $h_1=12 and h_2=15$ unit

Total volume of composite solid is $18 pi$ cubic unit.

Total volume of composite solid is

$V= pi*r^2*h_1+1/3*r^2*h_2$ or

$pi*r^2*12+1/3*r^2*15 = 18 pi$ or

$pi*r^2(12+5) = 18 pi$ or

$pi*r^2 = (18 pi) /17 ~~ 3.33$ sq.unit

Area of the base of cylinder is $A=pi*r^2~~ 3.33$ sq.unit [Ans]

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 15 15 and the height of the cylinder is 12 12 . If the volume of the solid is 18 pi18 pi, what is the area of the base of the cylinder?