If a circle has a radius of 3 cm, what is the length of an arc that subtends a c

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Question: If a circle has a radius of 3 cm, what is the length of an arc that subtends a central angle of 60 degrees?

Options:

Correct Answer: 3.77 cm

Solution:

Arc length = (θ/360) * 2πr = (60/360) * 2π(3) = (1/6) * 6π = π ≈ 3.14 cm.

If a circle has a radius of 3 cm, what is the length of an arc that subtends a central angle of 60 degrees?

If a circle has a radius of 3 cm, what is the length of an arc that subtends a central angle of 60 degrees?

Step 1: Identify the radius of the circle, which is given as 3 cm.
Step 2: Identify the central angle in degrees, which is given as 60 degrees.
Step 3: Use the formula for arc length: Arc length = (θ/360) * 2πr.
Step 4: Substitute the values into the formula: Arc length = (60/360) * 2π(3).
Step 5: Simplify the fraction 60/360 to 1/6.
Step 6: Calculate 2π(3) to get 6π.
Step 7: Multiply (1/6) by 6π to get π.
Step 8: The final answer for the arc length is π, which is approximately 3.14 cm.

Arc Length Calculation – The formula for calculating the length of an arc based on the radius and the central angle in degrees.
Understanding Central Angles – The relationship between the central angle and the fraction of the circle represented by the arc.