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What is the length of an arc of a circle with a radius of 4 cm and a central ang

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Question: What is the length of an arc of a circle with a radius of 4 cm and a central angle of 90 degrees? (2021)

Options:

  1. 2π cm
  2. 4π cm
  3. π cm
  4. 8 cm

Correct Answer: 2π cm

Solution: 

Arc length = (θ/360) * 2πr = (90/360) * 2π * 4 = 2π cm.

What is the length of an arc of a circle with a radius of 4 cm and a central ang

Practice Questions

Q1
What is the length of an arc of a circle with a radius of 4 cm and a central angle of 90 degrees? (2021)
  1. 2π cm
  2. 4π cm
  3. π cm
  4. 8 cm

Questions & Step-by-Step Solutions

What is the length of an arc of a circle with a radius of 4 cm and a central angle of 90 degrees? (2021)
  • Step 1: Identify the radius of the circle, which is given as 4 cm.
  • Step 2: Identify the central angle in degrees, which is given as 90 degrees.
  • Step 3: Use the formula for arc length: Arc length = (θ/360) * 2πr.
  • Step 4: Substitute the values into the formula: Arc length = (90/360) * 2π * 4.
  • Step 5: Simplify the fraction 90/360 to get 1/4.
  • Step 6: Calculate the arc length: Arc length = (1/4) * 2π * 4.
  • Step 7: Multiply: Arc length = 2π cm.
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