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 #12 # and the height of the cylinder is #28 #. If the volume of the solid is #72 pi#, what is the area of the base of the cylinder?

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Answer 1 · 2016-03-18T07:41:05

Area of base #= pir^2 = (9pi)/4#

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#color(red)("Total volume = volume of cone + volume of cylinder" = 72 pi)#

volume of cone #= 1/3 pi r^2 h = 12/3pir^2 = 4*pir^2#

Volume of cylinder# = pi r^2 h = pi r^2 * 28#

Total volume# = 32pir^2 = 72 pi#

#cancelpir^2 = 72/32cancel pi=9/4#

#=>r ^2 = 9/4#

Area of base #= pir^2 = (9pi)/4#