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. 8 in 45° 5.6 in. 6.3 in. 25.1 in.

Explanation:

Step1: Recall the 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 the values of \( \theta \) and \( r \)

From the diagram, the central angle \( \theta = 45^{\circ} \) and the radius \( r = 8 \) in. We are given \( \pi\approx3.14 \).

Step3: Substitute the values into the formula

First, calculate \( 2\pi r \): \( 2\times3.14\times8 = 50.24 \) in (this is the circumference of the circle). Then, find the fraction of the circumference corresponding to the arc: \( \frac{45^{\circ}}{360^{\circ}}=\frac{1}{8} \). Now, multiply this fraction by the circumference: \( s=\frac{1}{8}\times50.24 = 6.28 \).

Step4: Round to the nearest tenth

Rounding \( 6.28 \) to the nearest tenth gives \( 6.3 \).

Answer:

6.3 in