The formula for the circumference of a circle is C=πd

Question

, where C=
circumference and d=
diameter. It can also be defined as C=2πr
, where r=
radius. If 360 degrees =2π
radians, and the formula for arc length is θ=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.(4 points)

Answer 1

To find the arc length created by a 60-degree central angle in a circle with a 2-inch diameter, we can first convert the angle from degrees to radians. Since $360$ degrees is equal to $2\pi$ radians, we can find that $60$ degrees is equivalent to $\frac{60}{360}\times 2\pi =\frac{\pi }{3}$ radians.

Next, we calculate the radius $r$ of the circle, which is half of the diameter: $r=\frac{2}{2}=1$ inch. Using the formula for arc length $s=r\cdot \theta$, we substitute $r=1$ inch and $\theta =\frac{\pi }{3}$ radians to get the arc length:

$$s=1\cdot \frac{\pi }{3}=\frac{\pi }{3}\text{ inches}.$$

Therefore, the length of the arc is $\frac{\pi }{3}$ inches.