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    Question

    The dimensions of a cuboidal box are in the ratio 8:4:3 for

    its length, breadth, and height respectively. If the total surface area of the box is 2,176 cm², what is its lateral surface area?
    A 1,536 sq cm Correct Answer Incorrect Answer
    B 1,152 sq cm Correct Answer Incorrect Answer
    C 1,024 sq cm Correct Answer Incorrect Answer
    D 2,592 sq cm Correct Answer Incorrect Answer

    Solution

    Total surface area of cuboid = 2 X {(Length X breadth) + (Length X height) + (Height X breadth) }

    Let the length, breadth, and height of the cuboid be '8x' cm, '4x' cm, and '3x' cm, respectively.

    Total surface area of the given cuboid = 2 X {(8x X 4x) + (4x X 3x) + (8x X 3x) } = 2176

    Or, 32x 2  + 12x 2  + 24x 2  = (2176/2)

    Or, 68x 2  = 1088

    Or, x 2  = (1088/68) = 16

    Since the dimensions of a cuboid cannot be negative, x = 4

    Therefore, lateral surface area of the cuboid = 2 X (length + breadth) X height

    Or, required lateral surface area = 2 X (8x + 4x) X 3x = 72x 2  = 72 X 16 = 1152 cm 2

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