A semi-circular shaped window has diameter of 63 cm. Its perimeter equals

### Concept & Perimeter of a Semi-Circle The perimeter of a closed semi-circular shape (like a window) consists of the curved arc plus the straight edge (the diameter). $$ \text{Perimeter} = \pi r + 2r = r(\pi + 2) $$ ### Step-by-Step Solution * **Find the radius:** The given diameter $d = 63$ cm. Radius $r = \frac{63}{2}$ cm. (Leave as fraction for easier cancellation) * **Apply the perimeter formula:** $\text{Perimeter} = \frac{22}{7} \times \left(\frac{63}{2}\right) + 63$ * **Calculate the curved part:** $\frac{22}{7} \times \frac{63}{2} = 11 \times 9 = 99$ cm. * **Add the straight edge (diameter):** $\text{Total Perimeter} = 99 + 63 = 162$ cm. ### Exam Strategy & Shortcut Using the factored formula $P = r(\pi + 2) = r(\frac{22}{7} + \frac{14}{7}) = r(\frac{36}{7})$. Substitute $r = \frac{63}{2}$: $P = \frac{63}{2} \times \frac{36}{7} = 9 \times 18 = 162$. This is much faster. ### Common Pitfall Calculating only the curved boundary ($\pi r = 99$) and failing to add the flat bottom of the window ($d = 63$). ### Final Answer Therefore, the correct answer is **162 cm**.