I've got this problem: I have a cone (cone $A$) with a radius $8$ and a height of $12$. Now lets say that cone $A$ has a thickness of $2$. This thickness can be found from the bottom and inward and from the sides inward as well. I need to find the volume of the shell that is remaining. I do not yet know the height of the middle cone, only its radius. I've attached a look-alike picture to help give an idea. Any help is appreciated!
Imagine it like this, but with the cone in the middle being the thickness ($2$) inwards (up inside the other cone):
