Saved Bookmarks
| 1. |
The circumference of a circle is 8 cm. Find the area of the sector whose central angle is 72°. |
|
Answer» Let the radius of the circle is r cm. Given that the circumference of the circle is \(2{\pi}r\) = 8cm. \(\therefore\) \(r = \frac{8}{2\pi} = \frac{4}{\frac{22}{7}} = \frac{14}{11 }cm.\) ∵ Area of the circle is 2 \(\because\) Area of the sector whose central angle is 360° = \(\pi r^2\) cm2. \(\therefore\) Area of the sector whose central angle is 1° = \(\frac{\pi r^2}{360^°} cm^2\). \(\therefore\) Area of the sector whose central angle is 72°=\(\frac{\pi r^2}{360^°} \) x 72° cm2 \(\frac{22}{7} \times \frac{14}{11} \times \frac{14}{11}\times \frac{72}{360}\) \( = 2 \times 2 \times \frac{14}{11} \times \frac{1}{5} = \frac{56}{55} = 1.02 \,cm^2.\) Hence, the area of the sector whose central angel is 72° is 1.02 cm2 . |
|