Question

determine the angle at the center of a circle with radius 6.0 cm for an arc length of 8.0 cm.

• $dfrac{4}{3}$ radians
• $dfrac{2}{3}$ radians
• $dfrac{3}{4}$ radians
• $dfrac{pi}{12}$ radians

Explanation:

Step1: Recall arc length formula

The formula for arc length \( s \) is \( s = r\theta \), where \( r \) is the radius and \( \theta \) is the central angle in radians.

Step2: Solve for \( \theta \)

We know \( s = 8.0 \, \text{cm} \) and \( r = 6.0 \, \text{cm} \). Rearranging the formula gives \( \theta=\frac{s}{r} \). Substituting the values: \( \theta = \frac{8.0}{6.0}=\frac{4}{3} \) radians.

Answer:

\(\frac{4}{3}\) radians (the option: \(\boldsymbol{\frac{4}{3}}\) radians)