A solid cuboid has a length of 7 cm, a width of 5 cm, and a height of 4 cm. Calculate its total surface area.

Analyze the question: We need the total surface area of a cuboid with length l = 7 cm, width w = 5 cm and height h = 4 cm.

Concept: A cuboid has 6 rectangular faces, in 3 pairs of equal faces. The formula is:

Total Surface Area = 2(lw + lh + wh)

Solution:

• lw = 7 × 5 = 35
• lh = 7 × 4 = 28
• wh = 5 × 4 = 20

Sum = 35 + 28 + 20 = 83

Total Surface Area = 2 × 83 = 166 cm²

Check: The top and bottom faces give 2 × 35 = 70, the front and back give 2 × 28 = 56, and the two sides give 2 × 20 = 40. Then 70 + 56 + 40 = 166 cm². ✔

Answer: Option B, 166 cm².

Common trap: Option D (83 cm²) is only half the surface area, which is what you get if you forget to multiply by 2. Always double the sum, because each face has a matching opposite face.

Tip: Remember "2(lw + lh + wh)" as "three pairs of faces." Count the pairs, add them up, then double. Volume (l × w × h = 140 cm³) is a different quantity, and option C is a distractor based on it.