Find the perimeter of a sector (i.e., the curved portion as well as the two straight portions) of a circle of radius 14 cm and sector angle 75°.                                                                                                                                                        [Page No. 129]

Given, Radius = 14 cm, Sector angle = $75^\circ$

$$\text{Arc length} = 2\pi r \times \frac{\theta}{360^\circ}$$

$$= 2 \times \frac{22}{7} \times 14 \times \frac{75}{360}$$

$$= 2 \times \frac{22}{7} \times 14 \times \frac{5}{24}$$

$$=\frac{110}{6}=\frac{55}{3}\thickapprox18.33\text{ cm}$$

Perimeter of sector = $\text{arc} + 2r$

$$= \frac{55}{3} + 2 \times 14$$

$$= \frac{55}{3} + 28$$

$$=\frac{139}{3}\thickapprox46.33\text{ cm}$$