# Frosty's Doom

Calculus Level pending

Frosty the snowman is made from two uniform spherical snowballs, of radii 2R and 3R. The smaller (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.

Determine the ratio of Frosty's volume to his initial volume when Frosty is half his initial height, as a common fraction in simplest form a/b. Your answer should be the value of a+b.

(Source: Advanced Problems in Mathematics by Stephen Siklos)

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