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 36 and the height of the cylinder is 6 . If the volume of the solid is 126 pi, what is the area of the base of the cylinder?
1 Answer
Mar 22, 2016
Explanation:
The volume of the cylinder is given by its height multiplied by the area of its circular base.
V_"cylinder" = pi * r^2 * h_"cylinder"
h_"cylinder" = 6 in this question.
The volume of a cone is given by a third of its height multiplied by the area of its circular base.
V_"cone" = 1/3 * pi * r^2 * h_"cone"
h_"cone" = 36 in this question.- The variable
r is reused as the cone has the same radius as the cylinder.
The volume of the entire 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 * (6 + 1/3 xx 36)
Now it becomes a simple matter to solve for the base area of the cylinder, which is just
pi * r^2 = V_"solid"/(6 + 1/3 xx 36)
= (126pi)/18
=7pi
~~ 21.991
