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Frosty the snowman is made from two uniform spherical snowballs, of initial 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 both snowballs. During melting each snowball remains spherical and uniform.
Are the assumptions in this question reasonable? In what ways might the question be modified to make it more realistic?
Can you think of any other questions to ask about Frosty's plight?
Frosty the snowman appears again in A Frosty Puddle.
Adapted from STEP Mathematics I, 1991, Q2. Question reproduced by kind permission of Cambridge Assessment Group Archives. The question remains Copyright University of Cambridge Local Examinations Syndicate ("UCLES"), All rights reserved.