What is the length of an arc of a circle with a radius of 5 cm that subtends an

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Question: What is the length of an arc of a circle with a radius of 5 cm that subtends an angle of 60 degrees at the center?

Options:

Correct Answer: 5.24 cm

Solution:

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

What is the length of an arc of a circle with a radius of 5 cm that subtends an angle of 60 degrees at the center?

What is the length of an arc of a circle with a radius of 5 cm that subtends an angle of 60 degrees at the center?

Step 1: Identify the radius of the circle. In this case, the radius (r) is 5 cm.
Step 2: Identify the angle subtended at the center of the circle. Here, the angle (θ) is 60 degrees.
Step 3: Use the formula for the length of an arc, which is L = (θ/360) * 2πr.
Step 4: Substitute the values into the formula. So, L = (60/360) * 2π(5).
Step 5: Simplify the fraction 60/360 to 1/6.
Step 6: Calculate 2π(5) which equals 10π.
Step 7: Now, multiply (1/6) by 10π to get L = (1/6) * 10π.
Step 8: This simplifies to L = 10π/6, which can be further simplified to 5π/3.
Step 9: To find a numerical approximation, calculate 5π/3, which is approximately 5.24 cm.

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