(i) Frosty the Snowman is made from two uniform spherical snowballs, initially of radii 2R and 3R. The smaller one (which is his head) stands on top of the larger. As each snowball melts, its volume decreases at a rate which is directly proportional to its surface area, the constant of proportionality being the same for each snowball. During melting, the snowballs remain spherical and uniform.
When Frosty is half his original height, show that the ratio of his volume to his initial volume is 37/224
(ii) What is the ratio when Frosty is one tenth of his initial height?