Calculate the length of the arc of a circle if:

(A) the radius is 3.5 cm and the angle at the centre is 60°, and

(B) the radius is 6.3 m and the angle at the centre is 120°.                                                                                            [Page No. 129]

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

(A) $r = 3.5 \text{ cm}, \theta = 60^\circ$:

$$L = 2 \times \frac{22}{7} \times 3.5 \times \frac{60}{360}$$

$$L = 2 \times \frac{22}{7} \times 3.5 \times \frac{1}{6}$$

$$L = \frac{154}{42} = \frac{11}{3} = 3.67 \text{ cm}$$

(B) $r = 6.3 \text{ m}, \theta = 120^\circ$:

$$L = 2 \times \frac{22}{7} \times 6.3 \times \frac{120}{360}$$

$$L = 2 \times \frac{22}{7} \times 6.3 \times \frac{1}{3}$$

$$L = \frac{277.2}{21} = 13.2 \text{ m}$$