Question

practice problems:

1. find the length of the arc intercepted by a central angle of \\(\frac{2pi}{3}\\) radians in a circle with a radius of 9 cm.

Explanation:

Step1: Recall arc length formula

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

Step2: Substitute values

Given \( r = 9 \) cm and \( \theta = \frac{2\pi}{3} \), calculate \( s = 9 \times \frac{2\pi}{3} \).

Step3: Simplify the expression

\( 9 \times \frac{2\pi}{3} = 3 \times 2\pi = 6\pi \).

(Note: If a numerical approximation is needed, \( 6\pi \approx 18.85 \) cm, but the exact value is \( 6\pi \) cm.)

Answer:

6π cm