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 $5$ . If the volume of the solid is $226 pi$ , what is the area of the base of the cylinder?

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Answer 1 · 2018-05-22T12:08:06

Area of the base of cylinder is $44.37$ sq.unit.

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

Height of cylinder and cone are $h_c=5 , h_(cn) =33$ unit

Volume of cylinder is $V_c=pi*r^2*h_c=5 pi r^2$

Volume of cone is $V_(cn)=1/3pi*r^2*h_(cn)=1/3*33 pi r^2$ or

$V_(cn)=11 pi r^2 :.$ Volume of composite solid is

$V = 5pir^2+11pir^2 =16 pi r^2$ , which is equal to $226 pi$

$:.16 cancel pi r^2= 226 cancelpi :. r^2= 226/16=113/8$

$:. r= sqrt(113/8) ~~ 3.7583$ . Area of the base of cylinder is

$A=pi* r^2= pi* 113/8 ~~ 44.37(2 dp)$ 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 33 33 and the height of the cylinder is 5 5 . If the volume of the solid is 226 pi226 pi, what is the area of the base of the cylinder?