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 #42 # and the height of the cylinder is #1 #. If the volume of the solid is #480 pi#, what is the area of the base of the cylinder?

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Answer 1 · 2017-02-20T12:36:41

The area of the base #=32pi=100.5u^2#

Let #a=# area of the base

Volume of cone is #V_(co)=1/3*a*h_(co)#

Volume of cylinder is #V_(cy)=a*h_(cy)#

Total volume

#V=V_(co)+V_(cy)#

#V=1/3ah_(co)+ah_(cy)#

#480pi=a(1/3*42+1)#

#480pi=a*15#

#a=480/15pi=32pi#

#a=100.5#