Imagine an open-topped water tank 2 metres square made of a given thickness of
galvanised metal. If the cost of the tank were seen purely in terms of its constituent
materials, then cost would be represented by the cost of 20 square metres of galvanised
metal (i.e. five sides multiplied by 4 square metres). However, the
productivity of the tank should be seen in terms of its cubic capacity, 8 cubic
metres (i.e. 2 metres cubed).
If we increase the size of the tank to 4 metres square, then material cost rises to 80
square metres (a fourfold cost increase), yet cubic capacity rises to 64 cubic metres
(an eightfold increase in productivity). The material in the large tank compared to
the smaller therefore halves from 2.5 to 1.25 square metres of galvanised metal per
cubic unit of capacity. So long as the large tank uses the same thickness of material,
and construction costs are not dissimilar with large tanks, the relationship between
surface area and volume represents a clear saving.