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 #42 # and the height of the cylinder is #1 #. If the volume of the solid is #320 pi#, what is the area of the base of the cylinder?

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Answer 1 · 2016-07-16T02:36:58

#{64 pi}/3#

We use the formulas #V = 1/3 pi r^2 h# and #V = pi r^2 h# for the volumes of a cone and a cylinder, respectively. This gives us

#1/3 pi r^2 42 + pi r^2 1 = 320 pi#

or

#15 pi r^2= 320 pi#

So,

#r^2 = {320}/15 = 64/3#

and the area of the base of the cylinder is given by #pi r^2#