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  1. #1
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    helpp

    How does the surface area of a rectangular prism change if each of the dimensions is doubled?
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  2. #2
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    Quote Originally Posted by rose1 View Post
    How does the surface area of a rectangular prism change if each of the dimensions is doubled?
    Hi rose,

    It would increase by a factor of 4.

    If the the dimensions of the base are a and b with height c,

    SA_1 = 2ab + 2bc + 2ac

    SA_1=2(ab+bc+ac)

    Double the dimensions:

    SA_2 = 2(2a \cdot 2b)+2(2b \cdot 2c)+2(2a \cdot 2c)

    SA_2=8ab+8bc+8ac

    SA_2=8(ab+bc+ac)

    SA_2=4(SA_1)

    SA_2 is 4 times SA_1.

    Example:

    Let each edge = 1

    SA_1=2(1 \cdot 1)+2(1 \cdot 1)+2(1 \cdot 1)

    SA_1 = 6

    Now double the edge to 2

    SA_1=2(2 \cdot 2)+2(2 \cdot 2)+2(2 \cdot 2)

    SA_2 = 24
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