Question

1. the diagram shows a sector of a circle of radius 4 units, formed from an angle of size 145°. find the length of the arc rounded to two decimal places. arc length = units

Explanation:

Step1: Recall arc length formula

Arc length $L = 2\pi r \times \frac{\theta}{360^\circ}$, where $r=4$, $\theta=145^\circ$.

Step2: Substitute values

$L = 2\pi(4) \times \frac{145}{360} = 8\pi \times \frac{29}{72} = \frac{29\pi}{9}$.

Step3: Calculate and round

$\frac{29\pi}{9} \approx \frac{29 \times 3.1416}{9} \approx \frac{91.1064}{9} \approx 10.12$.

Answer:

10.12