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 #8 #. If the volume of the solid is #64 pi#, what is the area of the base of the cylinder?

1 Answer
Nov 16, 2016

20.1

Explanation:

A Conical Volume is given by:
#V = 1/3 * pi * r^2 * h#
A Cylindrical Volume is given by:
#V = pi * r^2 * h#
Circular Area (base of cylinder)
#A = 2*pi * r^2#

Total solid volume =
# 64pi = 1/3 * pi * r^2 * h_1 + pi * r^2 * h_2 #

Solve for r.
# 64 = 1/3 * r^2 * 36 + r^2 * 8# ; #64 = r^2 * 12 + r^2 * 8#
#64 = r^2 * 20# ; #64/20 = r^2# ;

#r^2# = 3.2 ; r = 1.79

#A = 2*pi * 3.2 = 20.1#