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15 October, 10:04

A box of crackers has a volume of 48 cubic inches. what is the volume of a similar box that is smaller by a scale factor of 2/3

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  1. 15 October, 10:14
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    For this case what you need to know is that the original volume of the cookie box is:

    V = (w) * (l) * (h)

    Where,

    w: width

    l: long

    h: height.

    We have then:

    V = (w) * (l) * (h) = 48 in ^ 3

    The volume of a similar box is:

    V = (w * (2/3)) * (l * (2/3)) * (h * (2/3))

    We rewrite:

    V = ((w) * (l) * (h)) * ((2/3) * (2/3) * (2/3))

    V = (w) * (l) * (h) * ((2/3) ^ 3)

    V = 48 * ((2/3) ^ 3)

    V = 14.22222222 in ^ 3

    Answer:

    the volume of a similar box that is smaller by a scale factor of 2/3 is:

    V = 14.22222222 in ^ 3
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