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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 #18 # and the height of the cylinder is #1 #. If the volume of the solid is #25 pi#, what is the area of the base of the cylinder?

Answer 1

Mason Adams

#(25pi)/7 ~~ 11.220#

The cylinder's height multiplied by the area of its circular base yields the volume of the cylinder.

#V_"cylinder" = pi * r^2 * h_"cylinder"#

A cone's volume can be calculated by multiplying the area of its circular base by one-third of its height.

#V_"cone" = 1/3 * pi * r^2 * h_"cone"#

The total volume of the solid is

#V_"solid" = V_"cylinder" + V_"cone"#

#= pi * r^2 * h_"cylinder" + 1/3 * pi * r^2 * h_"cone"#

#= pi * r^2 * (h_"cylinder" + 1/3 h_"cone")#

#= pi * r^2 * (1 + 1/3 xx 18)#

Now it becomes a simple matter to solve for the base area of the cylinder, which is just #pi r^2#.

#pi * r^2 = V_"solid"/(1 + 1/3 xx 18)#

#= (25pi)/7#

#~~ 11.220#

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