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 #36 # and the height of the cylinder is #4 #. If the volume of the solid is #144 pi#, what is the area of the base of the cylinder?

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Answer 1 · 2016-09-09T14:25:50

Base area of cylinder #=9pi#

As the cone and the cylinder have a same radius, their base area is also the same.

Let base area = A = #pir^2#.
cone volume #=pir^2xx(h1)/3#, (h1=36) = #Axx36/3 = 12A#
cylinder volume = #pir^2xxh2#, (h2=4) =#Axx4=4A#

solid volume = cone volume + cylinder volume
#144pi= 12A+4A = 16A#

#A =(144pi)/16 =9pi#