Help with Volume of a Cone

Please take a look at this problem here:

http://i54.tinypic.com/2nlvm7c.jpg

I'm trying to find the volume of the shaded part of the cone.
Normally, it would be 1/3 pi r squared H

and I would usually find the volume of the big cone and subtract it by the unshaded volume of the small cone to get the shaded volume. However, I don't think I can do it in this problem..

Please help!
If I know the answer, that would be helpful, too, but I'm not a great backward problem solver,
so I would love it if there is some work or explanation to get to the answer...

Thanks!

Your guess at how to solve it is correct! You need to find the area of the big cone and subtract the area of the small cone. To find the area of the cones, you need their heights and radii. You already have those values for the big cone, but you need to calculate it for the smaller cone. It's pretty easy to see that the height of the small cone is 3, but it's a little harder to find the radius of the small cone. Using similar triangles, the radius of the small cone is 2.

Now you can calculate it yourself!