Question

If the radius of a circle is 5 centimeters, how long is the arc subtended by an angle measuring 60°? A) 3 5 π cm B) 5 2 π cm C) 5 3 π cm D) 5 6 π cm

Answer 1

Answer:

The length of the arc is $\frac{5\pi}{3}$ centimeters.

Step-by-step explanation:

The length of an arc ($\Delta s$) with a given central angle is determined by the following expression:

$\Delta s = \frac{\theta}{360^{\circ}}\cdot 2\pi\cdot r$

Where:

$r$ - Radius, measured in centimeters.

$\theta$ - Central angle, measured in sexagesimal degrees.

Given that $r = 5\,cm$ and $\theta = 60^{\circ}$, then:

$\Delta s = \frac{60^{\circ}}{360^{\circ}} \times 2\pi \times 5\,cm$

$\Delta s = \frac{5\pi}{3}\,cm$

The length of the arc is $\frac{5\pi}{3}$ centimeters.