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25 March, 05:05

If 4,800 cm2 of material is available to make a box with a square base and an open top, find the largest possible volume of the box. Step 1 Let b be the length of the base and h the height. Then we must maximize the volume of the box, V

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  1. 25 March, 05:16
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    32000cm^3

    Explanation:

    Length L be base length

    h be the height

    Volume=V

    V=L^2h

    Surface area if box = L^2+4lh=4800

    Solving for h

    (4800-l^2/4L) = h

    1200L-L^3/4=h

    Substitute for h in V = L^2h

    v=1200L-L^3/4

    Differenting = 1200-3*L^2/4=0

    L=√ (1600) = 40

    Substitute L=40

    In V=1200L-L^3/4

    Hence 1200*40-40^4/4=32000cm^3
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