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 #39 # and the height of the cylinder is #17 #. If the volume of the solid is #120 pi#, what is the area of the base of the cylinder?

1 Answer
May 10, 2016

#pir^2 = 40pi#

Explanation:

This question is surprisingly simple, despite what look like awkward numbers.

#"Vol cone" = 1/3pir^2h# and # "Vol cylinder" = pir^2H#

Total volume = #1/3pir^2h + pir^2H = 120pi#

#1/3pir^2 39 + pir^2 17 = 120pirArr# #1/cancel3pir^2cancel39^13 + pir^2 17 = 120pi#

#13pir^2 + 17 pir^2 = 120pi#

# 30 pir^2 = 120pi" divide both sides by 30"#

#pir^2 = 40pi#

Nothing more is needed, because the area of the circular base is given by #pi r^2#.