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

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

Options:

Correct Answer: 5.24 cm

Solution:

The length of an arc is given by L = (θ/360) * 2πr. Here, r = 5 cm, so L = (60/360) * 2π(5) = (1/6) * 10π ≈ 5.24 cm.

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.

Arc Length Calculation – Understanding how to calculate the length of an arc using the formula L = (θ/360) * 2πr, where θ is the central angle in degrees and r is the radius of the circle.
Circle Properties – Knowledge of the relationship between diameter, radius, and the properties of circles, including how to derive the radius from the diameter.