An iron pipe $20$ cm long has exterior diameter equal to $25$ cm. If the thickness of the pipe is $1$ cm, then the whole surface of the pipe is

### Concept & Total Surface Area of Hollow Cylinder The whole surface area of a hollow pipe consists of the outer curved surface, the inner curved surface, and the areas of the two annular bases. $$ \text{TSA} = 2\pi R h + 2\pi r h + 2\pi(R^2 - r^2) = 2\pi(R+r)(h+R-r) $$ ### Step-by-Step Solution - **Given:** - Length $h = 20$ cm. - Exterior diameter $= 25$ cm, so outer radius $R = 12.5$ cm. - Thickness $= 1$ cm, so inner radius $r = 12.5 - 1 = 11.5$ cm. - **Calculation:** - Compute $(R+r) = 12.5 + 11.5 = 24$. - Compute $(h+R-r) = 20 + 12.5 - 11.5 = 21$. - $\text{TSA} = 2 \times \frac{22}{7} \times 24 \times 21$. - $\text{TSA} = 2 \times 22 \times 24 \times 3 = 44 \times 72 = 3168$ cm$^2$. ### Exam Strategy & Shortcut Using the factored formula $2\pi(R+r)(h+R-r)$ rather than computing each part separately saves significant time and reduces arithmetic errors. ### Common Pitfall Using the diameter instead of the radius for $R$ and $r$. ### Final Answer Therefore, the correct answer is **3168 cm²**.