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In a circle with center O, if the radius is 7 cm, what is the length of an arc s

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Question: In a circle with center O, if the radius is 7 cm, what is the length of an arc subtended by a central angle of 60 degrees?

Options:

  1. 7.33 cm
  2. 14.00 cm
  3. 8.00 cm
  4. 6.00 cm

Correct Answer: 7.33 cm

Solution: 

The length of an arc is given by L = (θ/360) * 2πr. Here, L = (60/360) * 2π(7) = (1/6) * 14π ≈ 7.33 cm.

In a circle with center O, if the radius is 7 cm, what is the length of an arc s

Practice Questions

Q1
In a circle with center O, if the radius is 7 cm, what is the length of an arc subtended by a central angle of 60 degrees?
  1. 7.33 cm
  2. 14.00 cm
  3. 8.00 cm
  4. 6.00 cm

Questions & Step-by-Step Solutions

In a circle with center O, if the radius is 7 cm, what is the length of an arc subtended by a central angle of 60 degrees?
  • Step 1: Identify the radius of the circle, which is given as 7 cm.
  • Step 2: Identify the central angle, which is given as 60 degrees.
  • Step 3: Recall the formula for the length of an arc: L = (θ/360) * 2πr.
  • Step 4: Substitute the values into the formula: L = (60/360) * 2π(7).
  • Step 5: Simplify the fraction 60/360 to 1/6.
  • Step 6: Calculate 2π(7) to get 14π.
  • Step 7: Multiply (1/6) by 14π to get (1/6) * 14π.
  • Step 8: This simplifies to 14/6π, which is approximately 7.33 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, central angles, and arc lengths.
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