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March 26, 2017

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Q. An open-top box with a square base is to have a volume of 62.5 square inches. What dimensions will yield the box of minimum surface area?

I am getting 5" by 2.5" but not sure.

  • Calculus - ,

    (s^2)h=V
    h=V/(s^2)=62.5/s^2
    Surface area = 4hs +s^2
    =4(62.5/s^2)s +s^2
    =250/s + s^2

    Derivative of surface area = -250/s^2 + 2s
    0=-250/s^2 + 2s
    250/s^2=2s
    250=2s^3
    125=s^3
    s=5
    h= 62.5/s^2=62.5/25 = 2.5
    You are correct!

  • Calculus - ,

    Thanks

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