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## 'Maths Filler' printed from http://nrich.maths.org/

A series of vessels of uniform cross section look like letters when
viewed face-on. They are 1cm thick, and the corners of the vessels
have either whole or half cm values for their coordinates.

Water is poured slowly into each vessel through one of the holes at
the top at a rate of 1 cm$^3$ per minute.

Seven of these vessels take the same time to fill up. Which are
they?

Which one takes the longest to fill?

Which would fill up first?

The height of the pool of water in one of the vessels is measured
and a chart of the height against time is plotted, as
follows:

Which vessel does this chart correspond to? Can you explain what
each part of the chart corresponds to?

The very observant solver might have noticed that the chart given
is actually slightly inaccurate: at certain points it is an
over-measurement and at certain points it is an under-measurement.
Can you see where and why?

Make charts of height against time for some of the other
letters.