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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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