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

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

Options:

  1. 3.14 cm
  2. 6.28 cm
  3. 12.56 cm
  4. 1.57 cm

Correct Answer: 3.14 cm

Solution: 

Arc length = (θ/360) * 2πr = (90/360) * 2π(4) = (1/4) * 8π = 2π ≈ 6.28 cm.

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

Practice Questions

Q1
What is the length of the arc of a circle with a radius of 4 cm and a central angle of 90 degrees?
  1. 3.14 cm
  2. 6.28 cm
  3. 12.56 cm
  4. 1.57 cm

Questions & Step-by-Step Solutions

What is the length of the arc of a circle with a radius of 4 cm and a central angle of 90 degrees?
  • Step 1: Identify the radius of the circle, which is given as 4 cm.
  • Step 2: Identify the central angle, 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 1/4.
  • Step 6: Calculate 2π(4) to get 8π.
  • Step 7: Multiply (1/4) by 8π to get 2π.
  • Step 8: If needed, approximate 2π to get about 6.28 cm.
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