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 #10 #. If the volume of the solid is #200 pi#, what is the area of the base of the cylinder?

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Answer 1 · 2016-07-10T10:50:09

The area of the base of the cylinder (which is a circle with radius #r#) #=pir^2=25pi/3sq.unit#.

Suppose that the radius of cone #= r =# that of cylinder.

Therefore, volume #V# of the solid=volume of cone + that of cylinder

#=1/3*pi*r^2*#(height of cone)+#pi*r^2*#(height of cyl.)

#=1/3*pi*r^2*42+pi*r^2*(10)#

#=14pir^2+10pir^2#

#:. V=24pir^2#

But we are given that #V=200pi.#

Therefore, #24pir^2=200pi rArr pir^2=200pi/24=25pi/3.............(1)#

Hence, the area of the base of the cylinder (which is a circle with radius #r#) #=pir^2=25pi/3# sq.unit, by #(1).#