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    Question

    The dimensions of a cuboidal box are in the ratio 3:2:1.

    If the total volume of the box is 546.75 cm³, determine its lateral surface area.
    A 202.5 sq cm Correct Answer Incorrect Answer
    B 196.5 sq cm Correct Answer Incorrect Answer
    C 206.5 sq cm Correct Answer Incorrect Answer
    D 192.5 sq cm Correct Answer Incorrect Answer

    Solution

    Let the length, breadth and height of box be '3a', '2a' and 'a' cm respectively.

    So, 3a X 2a X a = 546.75

    Or, 6a 3  = 546.75

    Or, a 3  = 91.125

    Or, 'a' = 4.5

    Length of box = 3 X 4.5 = 13.5 cm

    Breadth of box = 2 X 4.5 = 9 cm

    Height of box = 4.5 cm

    Lateral surface area of box = 2 X (length + breadth) X height

    = 2 X (13.5 + 9) X 4.5 = 9 X 22.5 = 202.5 cm 2

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