Question : A square of side 3 cm is cut off from each corner of a rectangular sheet of length 24 cm and breadth 18 cm, and the remaining sheet is folded to form an open rectangular box. The surface area of the box is:
Option 1: 468 cm2
Option 2: 396 cm2
Option 3: 612 cm2
Option 4: 423 cm2
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Correct Answer: 396 cm 2
Solution : Length of rectangular sheet = 24 cm Breadth of rectangular sheet = 18 cm Side of cut-out square = 3 cm Length of the box $(l)$ = [24 – (3 + 3)] = 18 cm Breadth of the box $(b)$ = [18 – (3 + 3)] = 12 cm Height of the box $(h)$ = 3 cm Surface area of an open rectangular box = $lb + 2(bh + hl)$ = [18 × 12 + 2(12 × 3 + 3 × 18)] = [216 + 2(36 + 54)] = 216 + 180 = 396 cm 2 Hence, the correct answer is 396 cm 2 .
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