Question

If an arc of a circle of radius 10.5 cm, subtends an angle of 60° at the centre, then find the length of the arc.

Hint:

$10.5$ is often easier to calculate as $21/2$ when working with the fraction $22/7$.

Answer 1

Step 1: Understanding the Concept:
The length of an arc is the distance along the curved line of a circle. It is calculated as a fraction of the total circumference ($2\pi r$).
Step 2: Formula and Substitution:
Length of arc $l = \frac{\theta}{360} \times 2\pi r$ Given: $r = 10.5$ cm, $\theta = 60^\circ$. \[ l = \frac{60}{360} \times 2 \times \frac{22}{7} \times 10.5 \]
Step 3: Calculation:
\[ l = \frac{1}{6} \times 2 \times \frac{22}{7} \times \frac{21}{2} \] \[ l = \frac{1}{6} \times 2 \times 22 \times \frac{3}{2} \] \[ l = \frac{22 \times 3}{6} = \frac{66}{6} = 11 \text{ cm} \]
Step 4: Final Answer:
The length of the arc is 11 cm.