Question

An open tank with a square base and vertical sides is to be constructed from a metal sheet so as to hold a given quantity of water. Show that the cost of material will be least when depth of the tank is half of its width. If the cost is to be borne by nearby settled lower income families, for whom water will be provided, what kind of value is hidden in this question ?

Answer 1

 Let side of base = x and depth of tank = y

V = x²y

y = V/x²

(V = Quantity of water = constant)

Cost of material is least when area of sheet used is minimum