Question

The formula for the circumference of a circle is C=πd
𝐶
=
𝜋
𝑑
, where C=
𝐶
=
circumference and d=
𝑑
=
diameter. It can also be defined as C=2πr
𝐶
=
2
𝜋
𝑟
, where r=
𝑟
=
radius. If 360 degrees =2π
=
2
𝜋
radians, and the formula for arc length is θ=sr
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) simple

Answer 1

The circle has radius r = 1 inch (diameter 2 inches). Convert 60° to radians: 60° = 60·(π/180) = π/3. Use arc length formula s = rθ, so s = 1·(π/3) = π/3 inches. That is about 1.05 inches.