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The surface area and volume formulae are:
The rate of decrease of volume is proportional to the surface area is translated as:
If the initial volume is , then:
, where is the initial radius.
So when :
So, assuming we measure time in hours, when :
So the time taken for the remainder to melt is:
hours.If, after all, the phrase 'half the snowball' meant that the radius has been halved, then, of course the additional time taken would be one hour, since the radius is decreasing at a constant rate.