A solid consists of a cone on top of a cylinder with a radius equal to the cone. The height of the cone is #3 # and the height of the cylinder is #12 #. If the volume of the solid is #24 pi#, what is the area of the base of cylinder?

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Answer 1 · 2017-02-04T06:47:46

The answer is #=24/13pi#

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)#

#24pi=a(1/3*3+12)#

#24pi=a*13#

#a=24/13pi#