Question

1. a sector of a circle of diameter 13 cm is formed from an angle of size 54°. find the length of the arc rounded to two decimal places. arc length = enter your next step here cm

Explanation:

Step1: Calculate radius

Radius $r = \frac{\text{diameter}}{2} = \frac{13}{2} = 6.5$ cm

Step2: Compute arc length

Arc length formula: $l = 2\pi r \times \frac{\theta}{360^\circ}$
Substitute values: $l = 2\pi(6.5) \times \frac{54}{360} = 13\pi \times 0.15 \approx 6.1261$

Step3: Round to two decimals

$6.1261 \approx 6.13$

Answer:

6.13