HOW TO MAKE CISTERNS.
(
Patchwork Puzzles)
Our friend in the illustration has a large sheet of zinc, measuring
(before cutting) eight feet by three feet, and he has cut out square
pieces (all of the same size) from the four corners and now proposes to
fold up the sides, solder the edges, and make a cistern. But the point
that puzzles him is this: Has he cut out those square pieces of the
correct size in order that the cistern may hold the greatest possible
quantity of water? You see, if you cut them very small you get a very
shallow cistern; if you cut them large you get a tall and slender one.
It is all a question of finding a way of cutting put these four square
pieces exactly the right size. How are we to avoid making them too small
or too large?
Answer:
Here is a general formula for solving this problem. Call the two sides
of the rectangle a and b. Then
a + b - (a squared + b squared - ab)^1/2
---------------------------
6
equals the side of the little square pieces to cut away. The
measurements given were 8 ft. by 3 ft., and the above rule gives 8 in.
as the side of the square pieces that have to be cut away. Of course it
will not always come out exact, as in this case (on account of that
square root), but you can get as near as you like with decimals.
