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      Question

      The lateral surface area of a cube is 324 cm2

      . The length of a cuboid is 50% more than the side of the cube. The breadth of the cuboid is 9 cm less than its length and 20% less than its height. Find the total surface area of the cuboid.
      A 220 cm^2 Correct Answer Incorrect Answer
      B 334 cm^2 Correct Answer Incorrect Answer
      C 324 cm^2 Correct Answer Incorrect Answer
      D 226 cm^2 Correct Answer Incorrect Answer
      E 221 cm^2 Correct Answer Incorrect Answer

      Solution

      Let the length of the cube be ‘a’ cm
      According to the question,
      4a2 = 324
      => a2 = 81
      => a = 9
      Therefore, length of the cuboid = l = 1.50 × 9 = 13.5 cm
      Breadth of the cuboid = b = 13.5 – 9 = 4.5 cm
      Height of the cuboid = h = 4.5/0.8 = 5.625 cm
      Therefore, total surface area of the cuboid = 2(lb + bh + lh) = 2 × {(13.5 × 4.5) + (4.5 × 5.625) + (13.5 × 5.625)} = 324 cm2

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