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 #5 # and the height of the cylinder is #12 #. If the volume of the solid is #36 pi#, what is the area of the base of the cylinder?

1 Answer
Apr 23, 2016

I found #8.3# units of area.

Explanation:

The volume of the cone is:
#V_"cone"=1/3pir^2h_1#
The volume of th cylinder is:
#V_"cylimder"=pir^2h_2#
where the "hs" are the heights of the two solids:
We can write:
#36pi=V_"cone"+V_"cylimder"#
i.e.
#36pi=1/3pir^2h_1+pir^2h_2#
#36=1/3r^2*5+r^2*12#
#r^2[5/3+12]=36#
#r^2[41/3]=36#
#r=sqrt(3/41*36)=1.6#
and the area of the base will be:
#A=pir^2=8.3# u.a.