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If a circle has a radius of 3 cm, what is the length of an arc that subtends a c

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Question: If a circle has a radius of 3 cm, what is the length of an arc that subtends a central angle of 120 degrees?

Options:

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

Correct Answer: 4π/3 cm

Solution: 

Arc length = (θ/360) * 2πr = (120/360) * 2π(3) = (1/3) * 6π = 2π cm.

If a circle has a radius of 3 cm, what is the length of an arc that subtends a c

Practice Questions

Q1
If a circle has a radius of 3 cm, what is the length of an arc that subtends a central angle of 120 degrees?
  1. 2π cm
  2. π cm
  3. 6π/3 cm
  4. 4π/3 cm

Questions & Step-by-Step Solutions

If a circle has a radius of 3 cm, what is the length of an arc that subtends a central angle of 120 degrees?
  • Step 1: Identify the radius of the circle, which is given as 3 cm.
  • Step 2: Identify the central angle in degrees, which is given as 120 degrees.
  • Step 3: Use the formula for arc length: Arc length = (θ/360) * 2πr.
  • Step 4: Substitute the values into the formula: Arc length = (120/360) * 2π(3).
  • Step 5: Simplify the fraction 120/360 to 1/3.
  • Step 6: Calculate 2π(3) to get 6π.
  • Step 7: Multiply (1/3) by 6π to get 2π.
  • Step 8: Conclude that the length of the arc is 2π cm.
  • Arc Length Calculation – The formula for calculating the length of an arc based on the radius and the central angle in degrees.
  • Understanding Central Angles – The relationship between the central angle and the fraction of the circle it represents.
  • Proportional Relationships – Using proportions to relate the angle to the total degrees in a circle (360 degrees).
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