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?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 Â + 12x 2 Â + 24x 2 Â = (2176/2)
Or, 68x 2 Â = 1088
Or, x 2 Â = (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 Â = 72 X 16 = 1152 cm 2
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