Question

a circle has a radius of 10 inches. find the approximate length of the arc intersected by a central angle of \\(\frac{2pi}{3}\\)
6.67 inches
10.47 inches
20.94 inches
62.8 inches
done

Explanation:

Step1: Recall arc length formula

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

Step2: Substitute values

Given \( r = 10 \) inches and \( \theta=\frac{2\pi}{3} \) radians. Substitute into the formula: \( s = 10\times\frac{2\pi}{3}=\frac{20\pi}{3} \).

Step3: Approximate the value

Calculate \( \frac{20\pi}{3}\approx\frac{20\times3.1416}{3}\approx20.94 \) inches.

Answer:

20.94 inches (corresponding to the option "20.94 inches")