Question

solomon needs to justify the formula for the arc length of a sector. which expression best completes this argument?

the circumference of a circle is given by the formula c = πd, where d is the diameter.

because the diameter is twice the radius, c = 2πr.

if equally sized central angles, each with a measure of n°, are drawn, the number of sectors that are formed will be equal to $\frac{360^{circ}}{n^{circ}}$

the arc length of each sector is the circumference divided by the number of sectors, or

therefore, the arc length of a sector of a circle with a central angle of n° is given by $2pi rcdot\frac{n}{360}$ or $\frac{pi rn}{180}$

Explanation:

Step1: Recall circumference formula

$C = 2\pi r$

Step2: Recall number - of - sectors formula

Number of sectors $=\frac{360}{n}$

Step3: Calculate arc - length formula

Arc length $=\frac{C}{\frac{360}{n}}=\frac{2\pi r}{\frac{360}{n}}=\frac{2\pi r\times n}{360}=\frac{\pi rn}{180}$

Answer:

$\frac{\pi rn}{180}$