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A circle has a radius of 5 cm. What is the length of an arc that subtends a cent

Practice Questions

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)
  1. 5.24 cm
  2. 10.47 cm
  3. 3.14 cm
  4. 6.28 cm

Questions & Step-by-Step Solutions

A circle has a radius of 5 cm. What is the length of an arc that subtends a central angle of 60 degrees? (2021)
  • 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.
  • Arc Length Calculation – The formula for calculating the length of an arc based on the radius and the central angle in degrees.
  • Understanding Degrees – Recognizing that the central angle is given in degrees and how it relates to the full circle (360 degrees).
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