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 #9 # and the height of the cylinder is #7 #. If the volume of the solid is #42 pi#, what is the area of the base of the cylinder?

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Answer 1 · 2017-01-01T09:11:57

The area of the base #=4.2pi=13.2 (unit)^2#

Volume of the cone is #=1/3*a*h#

Where,

#a=#area of the base

#h=# height of the cone #=9#

Volume of the cylinder is #=a*H#

where

#H=# height of the cylinder #=7#

Total volume

#V=1/3*a*h+a*H=42pi#

Therefore,

#a(h/3+H)=42pi#

#a(9/3+7)=42pi#

#10a=42pi#

#a=42/10pi=4.2pi=13.2 (unit)^2#