Half of a snowball melts in an hour, how long will it take for the rest to melt? assuming that it remains spherical and that its volume decreases at a rate proportional to its surface area.

Much appreciated(Headbang)

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- July 14th 2010, 01:47 AMzcus05Melting snowball at rate proportional to surface area?
Half of a snowball melts in an hour, how long will it take for the rest to melt? assuming that it remains spherical and that its volume decreases at a rate proportional to its surface area.

Much appreciated(Headbang) - July 14th 2010, 02:58 AMGrandad
Hello zcus05

Welcome to Math Help Forum!I am assuming the the phrase 'half of a snowball' refers to half the volume, not that the radius has been halved (which would reduce the volume to one-eighth of its original value).

The surface area and volume formulae are:

, where is the initial radius.

So when :

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.

Grandad

- July 15th 2010, 10:46 PMzcus05
Ive spent days trying to get my head around this problem, thanks heaps for the clear and comprehensive response (Rofl)