Answer :
The rectangular closed cistern that shall hold a
given
quantity of water
and yet have the smallest possible surface of metal must be a perfect
cube—that is, a cistern every side of which is a square.
For
1,000 cubic
feet of water the internal dimensions will be 10 ft. × 10 ft.
× 10 ft.,
and the zinc required will be 600 square feet.
In the case of a cistern
without a top the proportions will be exactly half a cube.
These are
the
"exact proportions" asked for in the second case.
The exact dimensions
cannot be given, but 12.6 ft. × 12.6 ft. × 6.3 ft.
is a close
approximation.
The cistern will hold a little too much water, at which
the buyer will not complain, and it will involve the plumber in a
trifling loss not worth considering.
