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What is the length of an arc of a circle with radius 5 cm and central angle 60 d
What is the length of an arc of a circle with radius 5 cm and central angle 60 degrees? (2023)
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Practice Questions
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Q1
What is the length of an arc of a circle with radius 5 cm and central angle 60 degrees? (2023)
5π/3 cm
5π/6 cm
5π/12 cm
5π/4 cm
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Arc length = (θ/360) × 2πr = (60/360) × 2π(5) = (1/6) × 10π = 5π/6 cm.
Questions & Step-by-step Solutions
1 item
Q
Q: What is the length of an arc of a circle with radius 5 cm and central angle 60 degrees? (2023)
Solution:
Arc length = (θ/360) × 2πr = (60/360) × 2π(5) = (1/6) × 10π = 5π/6 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) to get 10π.
Step 7: Multiply (1/6) by 10π to get (1/6) × 10π = 10π/6.
Step 8: Simplify 10π/6 to 5π/3 cm.
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