An open water tank of square base and vertical sides is to be constructed. If a given volume of water is to be stored, the cost of the sheet is minimum when the depth of the tank is:

An open water tank of square base and vertical sides is to be constructed. If a given volume of water is to be stored, the cost of the sheet is minimum when the depth of the tank is:

• A. Half of its width
• B. Equal to its width
• C. Twice its width
• D. One-third of its width

Answer: A) Half of its width

Explanation: Let base be x and depth h. V = x²h. Area S = x² + 4xh = x² + 4V/x. dS/dx = 2x - 4V/x² = 0 → x³ = 2V = 2(x²h) → x = 2h. Depth h = x/2 (half its width).