The formula for the circumference of a circle is C=πd , 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=sr , 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.
1 answer
To find the length of the arc created by a 60-degree central angle in a circle with a 2-inch diameter, we first need to find the circumference of the circle. The diameter is 2 inches, so the radius is 1 inch. Using the formula C = 2πr, we get C = 2π(1) = 2π inches. Since 360 degrees is equal to 2π radians, we can convert 60 degrees to radians by multiplying by π/180. So, 60 degrees is equivalent to π/3 radians. Finally, using the formula θ = sr, we find the arc length to be s = (π/3)(1) = π/3 inches, or about 1.05 inches.
3 answers