Final answer:
The length of a 60° arc in a circle with a 10 cm radius is found using the formula for the circumference, 2πr, and taking the fraction of the circle that the 60° represents. This gives an arc length of approximately 10.47 cm.
Step-by-step explanation:
Arc Length of a Circle with a Given Radius and Angle
To find the arc length of a 60° arc in a circle with a 10 centimeter radius, we can use the formula to calculate the arc length, which is a fraction of the circumference of the circle. The circumference of a whole circle is given by 2πr, where π is approximately 3.14159 and r is the radius of the circle. Since there are 360 degrees in a full circle, a 60° arc represents 60/360 or 1/6 of the full circle.
To calculate the arc length, we use the following steps:
- Calculate the circumference of the entire circle using the formula C = 2πr, where r is 10 centimeters.
- Multiply the circumference by the fraction of the circle that the arc represents. Since the arc is 60° and a full circle is 360°, the arc is 60/360 or 1/6 of the circle.
- The arc length is therefore (1/6) × C.
Substituting the given values, we have:
- Circumference, C = 2π(10 cm) = 20π cm
- Total arc length for a 60° arc is then (1/6) × 20π cm = 10/3π cm, which is approximately 10.47 cm.