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 #4 #. If the volume of the solid is #25 pi#, what is the area of the base of the cylinder?

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Answer 1 · 2017-01-19T06:49:37

The area of the base #=5/3pi#

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 is

#V_(co)+V_(cy)=1/3*a*h_(co)+a*h_(cy)=25pi#

So,

#a(1/3*33+4)=25pi#

#a*15=25pi#

#a=25/15pi=5/3pi#