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Open tank with a square base and given volume: dimensions for the least surface area

The same question, asked 3 times: 15 May 2023 S2, 10 May 2024 S1*, 22 Apr 2025 S2. Every wording below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    15 May 2023 S2

    105
    An open tank with a square bottom, to contain 4000 cubic cm. of liquid, is to be constructed. The dimensions of the tank, so that the surface area of the tank is minimum, are

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  2. Question 2

    10 May 2024 S1

    114
    Open metallic tank: square base, vertical sides, volume 500 m3^3. Dimensions for minimum metal area are

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  3. Question 3

    22 Apr 2025 S2

    140
    An open tank with a square bottom is to contain 4000 cubic cm. of liquid. The dimensions of the tank so that the surface area of the tank is minimum, is

    Tap an option to check your answer.