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. x 10 ft. x 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. x 12.6 ft. x 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.