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?

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