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 #24 # and the height of the cylinder is #4 #. If the volume of the solid is #90 pi#, what is the area of the base of the cylinder?

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Answer 1 · 2017-12-28T01:19:25

Base Area #= 23.56#

Combine the equations for the volumes of the cylinder and the cone to find the radius. Then calculate the base area (#pir^2#).

#V_"cone" = 1/3pir^2h#
#V_"cyl" = pir^2h#

#V = 90pi = 1/3pir^2h + pir^2h#

#90 = 1/3r^2xx24 + r^2xx4 = 12r^2#
#r^2 = 7.5#

Because we want #r^2# for the area anyway, we do not need to go further.
Base Area = #pir^2 = pixx7.5 = 23.56#