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    Question

    The edges of a rectangular box are in the ratio of 3 : 5

    : 8, and its surface area is 632 cm². What will be the volume of the box?
    A 801 cm³ Correct Answer Incorrect Answer
    B 990 cm³ Correct Answer Incorrect Answer
    C 510 cm³ Correct Answer Incorrect Answer
    D 960 cm³ Correct Answer Incorrect Answer

    Solution

    Let the dimensions of the box be 3x, 5x, and 8x. Surface area = 2(lw + lh + wh) ⇒ 2((3x)(5x) + (3x)(8x) + (5x)(8x)) = 632 ⇒ 2(15x2 + 24x2 + 40x2) = 632 ⇒ 2(79x2) = 632 ⇒ 158x2 = 632 ⇒ x2 = 4 ⇒ x = 2 Now, the dimensions of the box are 3x = 6 cm, 5x = 10 cm, and 8x = 16 cm. Volume = l × w × h ⇒ Volume = 6 cm × 10 cm × 16 cm ⇒ Volume = 960 cm3 The volume of the box is 960 cm3.

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