Question

what is the approximate length of arc s on the circle below? use 3.14 for π. round your answer to the nearest tenth. 5.6 in. 6.3 in. 14.3 in. 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 the arc represents: \( \frac{45^{\circ}}{360^{\circ}}=\frac{1}{8} \).
Now, multiply this fraction by the circumference (\( 2\pi r \)): \( s=\frac{1}{8}\times50.24 \).

Step4: Calculate the result

\( \frac{50.24}{8}=6.28 \approx 6.3 \) (rounded to the nearest tenth).

Answer:

6.3 in