The dimensions of a cuboid are 7cm, 11 cm and 13 cm. The total surface area is (Teachers' Exam, 2011)

### Concept & Total Surface Area of a Cuboid The total surface area encompasses the area of all six rectangular faces of the cuboid. $$\text{Total Surface Area (TSA)} = 2(lb + bh + hl)$$ ### Step-by-Step Solution * **Given:** Let length ($l$) = $13\text{ cm}$, breadth ($b$) = $11\text{ cm}$, and height ($h$) = $7\text{ cm}$ (order doesn't matter for TSA). * **Step 1: Calculate the area of each distinct pair of faces** $l \times b = 13 \times 11 = 143$ $b \times h = 11 \times 7 = 77$ $h \times l = 7 \times 13 = 91$ * **Step 2: Apply the TSA formula** $\text{TSA} = 2(143 + 77 + 91)$ $\text{TSA} = 2(311)$ $\text{TSA} = 622\text{ cm}^2$ ### Exam Strategy & Shortcut Check the unit digit of the sum before full calculation: $3 + 7 + 1 = 11$, so the sum ends in $1$. Multiplying by $2$ means the final answer must end in $2$. Options (b) and (d) end in $2$. Since the sum inside the bracket is around $300$, $2 \times 300 = 600$. This instantly points to $622$. ### Common Pitfall Calculating only half the surface area ($lb + bh + hl = 311$) and forgetting to multiply by 2 (which is Option A). Always double the sum to account for all six faces! ### Final Answer Therefore, the correct answer is **622 cm²**.