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 36π, 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:
Vcone=13πr2h1
The volume of th cylinder is:
Vcylimder=πr2h2
where the "hs" are the heights of the two solids:
We can write:
36π=Vcone+Vcylimder
i.e.
36π=13πr2h1+πr2h2
36=13r25+r212
r2[53+12]=36
r2[413]=36
r=34136=1.6
and the area of the base will be:
A=πr2=8.3 u.a.