I have been trying to solve this problem for hours. I know the radius of the cone is tan15. I also know that the maximum volume of the cone is found by taking the derivative of the equation for the volume, which I got to be .071797. I am really confused on how to do the rest. Please Help!

I need some helpful hints on how to go about answering the following question:

You are to place a sphere of ice cream into a cone of height 1.

1)What radius of the sphere will give to most volume of ice cream inside the cone ( as opposed to above the cone) for a cone with a base angle of 30 degrees?

2)What percent of this sphere of most volume lies inside the cone?