If the radius and height of a right circular cylinder are 21 cm and 35 cm respectively, then the total surface area of the cylinder is

### Concept & Total Surface Area of Cylinder The total surface area (TSA) of a solid right circular cylinder encompasses the curved surface area plus the area of the two circular bases (top and bottom). $$\text{TSA} = 2\pi rh + 2\pi r^2 = 2\pi r(r + h)$$ ### Step-by-Step Solution 1. **Identify given dimensions:** - Radius, $r = 21 \text{ cm}$. - Height, $h = 35 \text{ cm}$. 2. **Apply the TSA formula:** - $\text{TSA} = 2 \times \frac{22}{7} \times 21 \times (21 + 35)$ 3. **Simplify the expression:** - Calculate the sum in the brackets: $(21 + 35) = 56$. - Cancel the $7$ with $21$: $\frac{21}{7} = 3$. - $\text{TSA} = 2 \times 22 \times 3 \times 56$ 4. **Calculate final value:** - $\text{TSA} = 132 \times 56$ - $132 \times 50 = 6600$ - $132 \times 6 = 792$ - $6600 + 792 = 7392 \text{ sq cm}$. ### Exam Strategy & Shortcut Use unit digit estimation if options allow it. The expression is $2 \times 22 \times 3 \times 56 \rightarrow$ focus on unit digits: $2 \times 2 \times 3 \times 6 = 4 \times 18 = 72$. The unit digit must be $2$. Unfortunately, all options end in $2$, so full multiplication or factoring is required. Breaking $132 \times 56$ into $(132 \times 100)/2 + 132 \times 6$ is a reliable fast method. ### Common Pitfall A frequent mistake is calculating only the Curved Surface Area ($2\pi rh$) instead of the Total Surface Area, or incorrectly adding the radius and height. ### Final Answer Therefore, the correct answer is **7392 sq cm**.