Re: How to Make Cisterns

.... Spoiler alert .....
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Not sure I get what exactly is the problem here, and being
uncomfortable with numbers, I went about it as follows.
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Let the side of the initial sheet be a. Now cut out the sqaures of
side x from the four corners and fold up the sticky bits. You have
an open cistern of side a-2x and height x. The volume is
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 V(x) = x(a-2x)^2
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dV/dx = 0 gives
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 a - 2x = 0 or a -  6x = 0
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The first answer is cute as with x = a/2 leaves with a zero
area base and,  naturally, a volume of zero.
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The second answer gives x = a/6

or a volume of a^3/9.