If a circle has a diameter of 10 cm, what is the length of an arc that subtends

If a circle has a diameter of 10 cm, what is the length of an arc that subtends a central angle of 60 degrees?

If a circle has a diameter of 10 cm, what is the length of an arc that subtends a central angle of 60 degrees?

Step 1: Identify the diameter of the circle, which is given as 10 cm.
Step 2: Calculate the radius of the circle. The radius (r) is half of the diameter, so r = 10 cm / 2 = 5 cm.
Step 3: Identify the central angle in degrees, which is given as 60 degrees.
Step 4: Use the formula for the length of an arc, which is L = (θ/360) * 2πr.
Step 5: Substitute the values into the formula. Here, θ = 60 degrees and r = 5 cm.
Step 6: Calculate the length of the arc: L = (60/360) * 2π(5).
Step 7: Simplify the fraction: 60/360 = 1/6.
Step 8: Now calculate L = (1/6) * 10π.
Step 9: Finally, approximate the value: L ≈ 5.24 cm.

No concepts available.