Loo
Roll Emergency You must have noticed that
rolls of toilet paper look healthily full for ages and ages, then seem to run
out all of a sudden when you’re alone in the house… The thing to do, of course,
is to make sure there’s a spare roll nearby whenever the current roll is
getting a bit low – but how can you tell that, simply from the thickness of
the remaining roll? The Problem: A typical new roll of
toilet paper is 12cm in diameter, of which the central cardboard tube makes up
the middle 4cm.
Assuming the paper
doesn’t get more squashed at either the outer or inner sections, you can
assume that the length of paper remaining is proportional to the volume of paper
remaining, and hence to the crosssectional area remaining... A If Desperate Dan’s loo roll has got down to half its original width (i.e. diameter of 6cm), what percentage of paper is actually left? B What is the diameter when half of the paper has been used?
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