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11 October, 02:25

An open box is to contain a volume of 3 cubic meters. Given that the material forthe sides of the box costs 6 per square meter and the material for the bottom costs 9per square meter, express the total costCof the box as a function of the lengthlandwidthw.

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  1. 11 October, 06:05
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    Answer: total cost = 36/w + 36/l + 9lw

    Step-by-step explanation:

    The formula for determining the volume of the rectangular box is expressed as

    Volume = lwh

    Where lwh represents the length, width and height of the box respectively.

    Since the volume of the box = 3cm³, then

    lwh = 3

    h = 3/lw

    Since the box is open, the surface area would be

    2lh + 2wh + lw

    Given that the material for the sides of the box costs 6 per square meter, the total cost for the sides is

    (2lh * 6) + (2wh * 6)

    Substituting h = 3/lw into the above expression, it becomes.

    (2l * 3/lw * 6) + (2w * 3/lw * 6)

    = 36/w + 36/l

    Since the material for the bottom costs 9per square meter, the total cost for the bottom is

    9 * lw = 9lw

    Therefore, the total cost of the box as a function of the length land width is

    36/w + 36/l + 9lw
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