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    Question

    A wooden cuboid has its dimensions in the ratio 4:3:2

    respectively. If its volume is 1536 cm³, then calculate its lateral surface area.
    A 448 cm² Correct Answer Incorrect Answer
    B 460 cm² Correct Answer Incorrect Answer
    C 435 cm² Correct Answer Incorrect Answer
    D 457 cm² Correct Answer Incorrect Answer

    Solution

    ATQ,

    Let the length, breadth and height of cuboid be ‘4a’, ‘3a’ and ‘2a’ cm respectively.

    So, 4a × 3a × 2a = 1536

    Or, 24a³ = 1536

    Or, a³ = 64

    Or, a = 4

    Length of cuboid = 4 × 4 = 16 cm

    Breadth of cuboid = 3 × 4 = 12 cm

    Height of cuboid = 2 × 4 = 8 cm

    Lateral surface area of cuboid = 2 × (length + breadth) × height= 2 × (16 + 12) × 8

    = 2 × 28 × 8 = 448 cm²

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