An open box is made from a square tin sheet of side 12 inches by cutting out equal squares of side x inches from each of the four corners and folding up the sides vertically. What integer value of x maximizes the volume of the box?

A tank with a rectangular base and rectangular sides, open at the top, is to be constructed so that its depth is 4 meters and its volume is 36 cubic meters. If building the tank costs ₹ 100 per square meter for the base and ₹ 50 per square meter for the sides, then the minimum cost of constructing the tank is:

An open metallic tank is to be constructed with a square base and vertical sides, having a volume of 500 cubic meters. The dimensions of the tank for the minimum area of the sheet metal used in its construction are: