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A circle has a radius of 5 cm. What is the length of an arc that subtends a cent
A circle has a radius of 5 cm. What is the length of an arc that subtends a central angle of 60 degrees? (2021)
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Practice Questions
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Q1
A circle has a radius of 5 cm. What is the length of an arc that subtends a central angle of 60 degrees? (2021)
5.24 cm
10.47 cm
3.14 cm
6.28 cm
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Arc length = (θ/360) * 2πr; = (60/360) * 2π * 5 = 10.47 cm.
Questions & Step-by-step Solutions
1 item
Q
Q: A circle has a radius of 5 cm. What is the length of an arc that subtends a central angle of 60 degrees? (2021)
Solution:
Arc length = (θ/360) * 2πr; = (60/360) * 2π * 5 = 10.47 cm.
Steps: 8
Show Steps
Step 1: Identify the radius of the circle, which is given as 5 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 * 5.
Step 5: Simplify the fraction 60/360 to 1/6.
Step 6: Calculate 2π * 5, which equals 10π.
Step 7: Multiply (1/6) by 10π to find the arc length: Arc length = (1/6) * 10π.
Step 8: Calculate the final value: Arc length ≈ 10.47 cm.
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