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]