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 #17 #. If the volume of the solid is #42 pi#, what is the area of the base of the cylinder?

Question

1031 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-11-23T16:20:17

Express the volume in function of the area of the base.

If A is the are of the common base:

#V_"cylinder" = A * h = 17A#
#V_"cone" = A * h / 3 = 33 * A / 3 = 11A#

Total volume is #(17A+11A) = 28A = 42pi#, so the are is:

#A= 42/28 * pi = 3/2*pi#