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 #12 # and the height of the cylinder is #18 #. If the volume of the solid is #72 pi#, what is the area of the base of the cylinder?

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Answer 1 · 2016-09-07T14:02:58

The area of the base is #36/11pi#.

Start by drawing a diagram.

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The formula for volume of a cone is # V= 1/3r^2hpi# and the formula for volume of a cylinder is #V = pir^2h#.

Let #V_t# denote the total volume.

#V_t = V_"cylinder" + V_"cone"#

#72pi = pir^2h + 1/3r^2hpi#

#72pi = 18pir^2 + 12(1/3r^2pi)#

#72pi = 18pir^2 + 4r^2pi#

#72pi = 22pir^2#

#36/11 = r^2#

#r = sqrt(36/11)#

#r = 6/sqrt(11)#

The formula for area of a circle is #A = pir^2#, so the area of the base is #A = (6/sqrt(11))^2pi = 36/11pi#.

Hopefully this helps!