Walter from Abingdon School in the UK sent in this full solution to the first part of the problem (click here to see a larger version):
Walter's solution to the second part of the problem is almost perfect (click here to see a larger version):
Once Walter realises that the top snowball is completely melted (and has a negative radius), Walter removes that snowball from the volume calculation - which is correct.
However, Walter should have recalculated the radius of the remaining snowball using the new information that the smaller snowball had disappeared.
What should the answer be?