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26 December, 22:33

Drum Tight Containers is designing an open-top, square-based, rectangular box that will have a volume of 1098.5 inches cubed. What dimensions will minimize surface area? What is the minimum surface area?

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  1. 26 December, 22:34
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    Area = s^2 + 4sh

    For minimum dA/ds = 2s + 4h = 0

    s = - 2h

    But s^2h = 1098.5

    (-2h) ^2 h = 1098.5

    4h^3 = 1098.5

    h^3 = 1098.5/4 = 274.625

    h = cube roof of 274.625 = 6.5 inches

    Thus, s^2 (6.5) = 1098.5

    s^2 = 169

    s = sqrt (169) = 13 inches

    Therefore, to minimize the surface area, the square base should have sides of 13 inches while the height should be 6.5 inches.

    Surface area = (13) ^2 + 4 (13 x 6.5) = 169 + 338 = 507 inches
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