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11 November, 23:41

A rectangular prism has side lengths of 4 inches, 6 inches, and 7 inches. If all side lengths are doubled, what happens to the surface area

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  1. 11 November, 23:58
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    Original measurements:

    L = 4; W = 6; H = 7

    surface area = 2 (LW + LH + HW)

    surface area = 2 (4 * 6 + 4 * 7 + 6 * 7)

    surface area = 2 (24 + 28 + 42)

    surface area = 2 (94)

    surface area = 188

    Doubled measurements:

    L = 8; W = 12; H = 14

    surface area = 2 (LW + LH + HW)

    surface area = 2 (8 * 12 + 8 * 14 + 12 * 14)

    surface area = 2 (96 + 112 + 168)

    surface area = 2 (376)

    surface area = 752

    The surface area was 188 square inches and it became 752 square inches.

    752/188 = 4

    As the side lengths increased by a factor of 2, the surface area increased by a factor of 4.
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