a rectangular prism has a volume of 112 cm every dimension of the rectangular prism is multiplied by a scale factor and the new volume is 1.

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a rectangular prism has a volume of 112 cm every dimension of the rectangular prism is multiplied by a scale factor and the new volume is 1.75 cm3 . what was the scale factor

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    2022-01-04T18:33:06+00:00

    The volume of the rectangular prism is

    l \times b \times h =112 cm^3

    Let the scale factor be

    k

    If we multiply each of the dimensions by k, then we have,

    lk, bk, hk

    as our new dimensions

    Then the new volume is

    lbh \times k^3 = 1.75 cm^3

    But

    lbh = 112 cm^3

    \Rightarrow 112 \times k^3 = 1.75 cm^3

    \Rightarrow k^3 =\frac{1.75}{112}

    \Rightarrow k^3 =\frac{1}{64}

    \Rightarrow k=\sqrt(\frac{1}{64})

    \Rightarrow k=\frac{1}{8}

     <B>Hence the scale factor is</B>

    \frac{1}{8}

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