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 #6 #. If the volume of the solid is #130 pi#, what is the area of the base of the cylinder?

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Answer 1 · 2016-12-15T06:15:57

The answer is #=45.4#

Let area of base #=a#

The volume of the cone #=1/3*a*h#

The volume of the cylinder #=a*H#

Total volume #V=1/3ah+aH=a(h/3+H)#

#V=130pi#

height of cone #h=9#

height of cylinder #H=6#

So,

#a(9/3+6)=130pi#

#9a=130pi#

#a=130/9pi=45.4#