Question

The formula for the circumference of a circle is C =πd, where C = circumference and the formula for arc length is 0 = s/r, then determine the length created by a 60-degree central angle in a circle with a 2-inch diameter and explain how you found it. Answer in 3-5 sentences.

Answer 1

To determine the arc length created by a 60-degree central angle in a circle with a 2-inch diameter, we first need to find the radius of the circle, which is half of the diameter: \( r = \frac{2 \text{ inches}}{2} = 1 \text{ inch} \). The formula for arc length \( s \) is given by \( s = \frac{\theta}{360} \times C \), where \( \theta \) is the central angle in degrees and \( C \) is the circumference of the circle.

First, we calculate the circumference using the formula \( C = \pi d = \pi \times 2 = 2\pi \text{ inches} \). Then we can find the arc length with \( s = \frac{60}{360} \times 2\pi = \frac{1}{6} \times 2\pi = \frac{1}{3}\pi \text{ inches} \). Therefore, the arc length created by the 60-degree central angle in the circle is approximately 1.05 inches.