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 #5 #. If the volume of the solid is #24 pi#, what is the area of the base of the cylinder?

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Answer 1 · 2018-06-28T20:37:48

#{3\pi}/2#

Let #r# be the radius of base of cone of height 33 & cylinder of height 5 then the volume of composite solid

#24\pi=\text{volume of cone of height 33 & radius r}+\text{volume of cylinder of height 5 & radius r}#

#24\pi=1/3\pir^2\cdot 33+\pir^2\cdot 5#

#24\pi=16\pi r^2#

#\pir^2={24\pi}/16#

#\pir^2={3\pi}/2#

#\therefore \text{area of base of the cylinder}={3\pi}/2#