Question

1. a sector has a central angle with a measure of 60° and an arc length of 10 cm. 5a find the radius of the sector, correct to two decimal places. radius = 9.55 cm 5b find the diameter of the sector, correct to two decimal places. diameter = cm

Explanation:

Step1: Recall arc length formula

Arc length $l = \frac{\theta}{360^\circ} \times 2\pi r$, where $\theta=60^\circ$, $l=10$ cm.

Step2: Substitute values and solve for $r$

$10 = \frac{60}{360} \times 2\pi r \implies 10 = \frac{1}{6} \times 2\pi r \implies 10 = \frac{\pi r}{3} \implies r = \frac{30}{\pi}$

Step3: Calculate radius

$r \approx \frac{30}{3.1416} \approx 9.55$ cm

Step4: Find diameter

Diameter $d = 2r = 2 \times 9.55 = 19.10$ cm

Answer:

9.55 cm (radius), 19.10 cm (diameter)