The length, breadth, and height of a cuboid are 10 cm, 6 cm, and 4 cm respectively. What is the total surface area of the cuboid (in square centimetres)?

Introduction / Context:
This question asks for the total surface area of a rectangular cuboid, a very common three dimensional shape in aptitude and geometry questions. The total surface area is the sum of the areas of all six rectangular faces, and the problem tests whether you know and can use the standard formula efficiently.

Given Data / Assumptions:

• Length l = 10 cm.
• Breadth b = 6 cm.
• Height h = 4 cm.
• We need the total surface area (TSA) in square centimetres.

Concept / Approach:
The total surface area of a cuboid with dimensions l, b, and h is given by: TSA = 2 * (l * b + b * h + h * l). This formula comes from adding the areas of the three distinct face rectangles (each appearing twice): l × b, b × h, and h × l. We substitute the given values and simplify.

Step-by-Step Solution:
Step 1: Compute the area of the base rectangle: l * b = 10 * 6 = 60 square centimetres. Step 2: Compute the area of the side rectangle: b * h = 6 * 4 = 24 square centimetres. Step 3: Compute the area of the front rectangle: h * l = 4 * 10 = 40 square centimetres. Step 4: Sum these three distinct face areas: 60 + 24 + 40 = 124. Step 5: Because each rectangle appears twice on opposite faces, multiply this sum by 2: TSA = 2 * 124 = 248 square centimetres.

Verification / Alternative check:
You can verify by listing all six faces explicitly:

• Two faces of size 10 × 6: 2 * 60 = 120.
• Two faces of size 6 × 4: 2 * 24 = 48.
• Two faces of size 4 × 10: 2 * 40 = 80.

Adding these gives 120 + 48 + 80 = 248 square centimetres, which matches our formula based calculation.

Why Other Options Are Wrong:
124 square centimetres is the sum of the three distinct face areas before doubling, so it counts each only once and underestimates the full surface area. 372 and 496 square centimetres would correspond to different combinations or mistaken multipliers and do not match the correct sum of all six faces. Only 248 square centimetres is consistent with properly counting every face exactly once.

Common Pitfalls:
A common mistake is to forget to multiply by 2 and thus only account for three faces instead of six. Another error is mixing up the dimensions or miscalculating one of the products l * b, b * h, or h * l. Writing all three products clearly and verifying them before doubling helps avoid these errors.

Final Answer:
The total surface area of the cuboid is 248 square centimetres.