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Jan says if you double each of the dimensions of a rectangular box, it will take twice as much wrapping paper to wrap it. How do you respond?

  • math -

    the surface area of a rectangular solid is given by
    SA = 2(LW + LH + WH)
    W = width, L = length, H = height
    if we double all the dimensions,
    SA' = 2[(2L)(2W) + (2L)(2H) + (2W)(2H)]
    SA' = 2[4LW + 4LH + 4WH]
    SA' = 2*4[LW + LH + WH]
    SA' = 4*SA

    therefore, what Jan says is wrong. It takes 4 times as much wrapping paper to wrap it.

    hope this helps~ :)

  • math -

    Since area is 2-dimensional, doubling each linear dimension scales the area by 22 = 4

    It changes the volume by 23 = 8

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