For a sector of a circle with radius $r$ and central angle $\theta$ in degrees, which formula gives the length of its arc?
A$\dfrac{\pi r^2\theta}{360}$
B$\dfrac{\pi r\theta}{180}$
C$2\pi r\theta$
D$\dfrac{r\theta}{2}$
Answer & Solution
Correct answer: B. $\dfrac{\pi r\theta}{180}$
Arc length is the same fraction of the full circumference as $\theta$ is of $360^\circ$. So $l=\dfrac{\theta}{360}\cdot 2\pi r=\dfrac{\pi r\theta}{180}$. Option A is the formula for the area of a sector, not its arc length.
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