Question

what is the approximate length of arc s on the circle below? use 3.14 for \\( \pi \\). round your answer to the nearest tenth. circle with radius 8 in and central angle 45° for arc s \\( \bigcirc \\) 5.6 in. \\( \bigcirc \\) 6.3 in. \\( \bigcirc \\) 14.3 in. \\( \bigcirc \\) 25.1 in.

Explanation:

Step1: Recall arc length formula

The formula for the length of an arc \( s \) is \( s=\frac{\theta}{360^\circ}\times2\pi r \), where \( \theta \) is the central angle in degrees and \( r \) is the radius of the circle.

Step2: Identify given values

Here, \( \theta = 45^\circ \), \( r = 8 \) in, and \( \pi\approx3.14 \).

Step3: Substitute values into formula

First, calculate \( 2\pi r \): \( 2\times3.14\times8 = 50.24 \) in.
Then, find the fraction of the circle: \( \frac{45^\circ}{360^\circ}=\frac{1}{8} \).
Multiply the two results: \( s=\frac{1}{8}\times50.24 = 6.28 \approx 6.3 \) in.

Answer:

6.3 in