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Open tank of given volume: dimensions for the least surface area

This type of question, asked 4 times: 15 May 2023 S2, 10 May 2024 S1, 22 Apr 2025 S2, 16 Apr 2026 S2. All 4 questions below, oldest first.

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  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

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  4. Question 4

    16 Apr 2026 S2

    74
    A cylindrical tank without a top lid is being manufactured to hold a fixed volume of 125π125\pi cubic cm. The minimum surface area required to construct this tank is ............square cm

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