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What is the length of an arc of a circle with radius 5 cm and central angle 60 d

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Question: What is the length of an arc of a circle with radius 5 cm and central angle 60 degrees? (2023)

Options:

  1. 5π/3 cm
  2. 5π/6 cm
  3. 5π/12 cm
  4. 5π/4 cm

Correct Answer: 5π/6 cm

Exam Year: 2023

Solution: 

Arc length = (θ/360) × 2πr = (60/360) × 2π(5) = (1/6) × 10π = 5π/6 cm.

What is the length of an arc of a circle with radius 5 cm and central angle 60 d

Practice Questions

Q1
What is the length of an arc of a circle with radius 5 cm and central angle 60 degrees? (2023)
  1. 5π/3 cm
  2. 5π/6 cm
  3. 5π/12 cm
  4. 5π/4 cm

Questions & Step-by-Step Solutions

What is the length of an arc of a circle with radius 5 cm and central angle 60 degrees? (2023)
  • 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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