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 #17 #. If the volume of the solid is #140 pi#, what is the area of the base of the cylinder?

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Answer 1 · 2017-11-16T01:52:31

#S=5pi#

The volume of a cylinder #V# is #V=Sh#, where #S# is the area of the base and #h# is the height.
The volume of a cone is #V=1/3Sh#.

Let #S# the area of the base in this solid.
The volume of the cone is #V_"co"=1/3*S*33=11S# and the volume of the cylinder is #V_"cy"=S*17=17S#

The total volume is #V=V_"co"+V_"cy"=11S+17S=28S#.
Therefore,
#28S=140pi#
#S=5pi#
is the required answer.