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.