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In a circle, if the radius is 10 cm, what is the length of an arc that subtends

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Question: In a circle, if the radius is 10 cm, what is the length of an arc that subtends a central angle of 60 degrees?

Options:

  1. 10.47 cm
  2. 6.28 cm
  3. 17.45 cm
  4. 5.24 cm

Correct Answer: 10.47 cm

Solution: 

The length of an arc is given by L = (θ/360) * 2πr. Here, L = (60/360) * 2π(10) = (1/6) * 20π ≈ 10.47 cm.

In a circle, if the radius is 10 cm, what is the length of an arc that subtends

Practice Questions

Q1
In a circle, if the radius is 10 cm, what is the length of an arc that subtends a central angle of 60 degrees?
  1. 10.47 cm
  2. 6.28 cm
  3. 17.45 cm
  4. 5.24 cm

Questions & Step-by-Step Solutions

In a circle, if the radius is 10 cm, what is the length of an arc that subtends a central angle of 60 degrees?
  • Step 1: Identify the radius of the circle, which is given as 10 cm.
  • Step 2: Identify the central angle in degrees, which is given as 60 degrees.
  • Step 3: Use the formula for the length of an arc, which is L = (θ/360) * 2πr.
  • Step 4: Substitute the values into the formula: L = (60/360) * 2π(10).
  • Step 5: Simplify the fraction 60/360 to 1/6.
  • Step 6: Calculate 2π(10) to get 20π.
  • Step 7: Multiply (1/6) by 20π to get (1/6) * 20π.
  • Step 8: The result is approximately 10.47 cm.
  • Arc Length Calculation – Understanding how to calculate the length of an arc using the formula L = (θ/360) * 2πr, where θ is the central angle in degrees and r is the radius.
  • Circle Properties – Knowledge of the properties of circles, including the relationship between radius, diameter, and arc length.
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