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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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