Question

8 what is the approximate length of the arc subtended by an angle of \\(\frac{4\pi}{3}\\) radians on a circle with a radius of 6.00 meters? a. 12.57 meters c 25.13 meters b 14.14 meters d 28.27 meters

Explanation:

Step1: Recall arc length formula

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

Step2: Identify given values

Here, \( r = 6.00 \) meters and \( \theta=\frac{4\pi}{3} \) radians.

Step3: Substitute values into formula

Substitute \( r = 6 \) and \( \theta=\frac{4\pi}{3} \) into \( s = r\theta \):
\( s=6\times\frac{4\pi}{3} \)
Simplify the expression: \( 6\times\frac{4\pi}{3}= 8\pi \)

Step4: Approximate the value

Using \( \pi\approx3.1416 \), we get \( 8\pi\approx8\times3.1416 = 25.1328 \approx25.13 \) meters.

Answer:

C. 25.13 meters