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What is the length of an arc of a circle with a radius of 10 cm and a central an
What is the length of an arc of a circle with a radius of 10 cm and a central angle of 60 degrees? (2021) 2021
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Practice Questions
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Q1
What is the length of an arc of a circle with a radius of 10 cm and a central angle of 60 degrees? (2021) 2021
10.47 cm
15.71 cm
20.94 cm
25.13 cm
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Arc length = (θ/360) * 2πr = (60/360) * 2 * 3.14 * 10 = 10.47 cm.
Questions & Step-by-step Solutions
1 item
Q
Q: What is the length of an arc of a circle with a radius of 10 cm and a central angle of 60 degrees? (2021) 2021
Solution:
Arc length = (θ/360) * 2πr = (60/360) * 2 * 3.14 * 10 = 10.47 cm.
Steps: 8
Show Steps
Step 1: Identify the radius of the circle. In this case, the radius (r) is 10 cm.
Step 2: Identify the central angle in degrees. Here, the central angle (θ) is 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) * 2 * π * 10.
Step 5: Simplify the fraction 60/360 to 1/6.
Step 6: Calculate 2 * π * 10, which is approximately 62.8 cm (using π ≈ 3.14).
Step 7: Multiply (1/6) by 62.8 cm to find the arc length: Arc length = 62.8 / 6.
Step 8: Perform the division: 62.8 / 6 = 10.47 cm.
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