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 #13 #. If the volume of the solid is #232 pi#, what is the area of the base of the cylinder?

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Answer 1 · 2016-11-15T09:24:53

The area of the base #=9.7pi#

Let the area of the base of cylinder #=a#

Then the area of the base of the cone #=a#

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

where #h# is the height of the cone

The volume of the cylinder is #=a*H#

where #H# is the height of the cylinder

The total volume is #=232pi#

then, #232pi=1/3*a*h+a*H#

But #h=33# and #H=13#

Therefore, #232pi=1/3*a*33+13a=24a#

#a=232pi/24=9.7pi#