IF a cone is inscribed in a larger cone,then what will be the radius of the small cone if it has the maximum volume? 

If a smaller cone is inscribed in a larger cone as shown, then what will be the radius of the smaller cone if it has the maximum volume?  

Attempt
I know that the volume of a cone =$\dfrac{1}{3}\pi r^2h$ , and the maximum volume can found by setting the derivative equal to zero to see where the maximum lies.
I tried to find a relation between the the height of the small cone and the larger cone to express h in terms of r in the equation of volume, but I got nothing.
Help.

You are on the right track.  Let $h$ be the height of the small cone.  Slice the cones with a vertical plane through the axis.  Each cone becomes an isosceles triangle.  If you draw the axis you have two right triangles.  Use the known shape of the large triangle to get the  base of the small triangle, which is the diameter of the small cone, as a function of $h$
