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In a circle, if the length of an arc is 10 cm and the radius is 5 cm, what is th

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Question: In a circle, if the length of an arc is 10 cm and the radius is 5 cm, what is the angle in radians subtended by the arc at the center? (2021)

Options:

  1. 1 rad
  2. 2 rad
  3. 3 rad
  4. 4 rad

Correct Answer: 2 rad

Exam Year: 2021

Solution: 

The angle in radians is given by the formula θ = s/r, where s is the arc length. Thus, θ = 10/5 = 2 rad.

In a circle, if the length of an arc is 10 cm and the radius is 5 cm, what is th

Practice Questions

Q1
In a circle, if the length of an arc is 10 cm and the radius is 5 cm, what is the angle in radians subtended by the arc at the center? (2021)
  1. 1 rad
  2. 2 rad
  3. 3 rad
  4. 4 rad

Questions & Step-by-Step Solutions

In a circle, if the length of an arc is 10 cm and the radius is 5 cm, what is the angle in radians subtended by the arc at the center? (2021)
  • Step 1: Identify the given values. The length of the arc (s) is 10 cm and the radius (r) is 5 cm.
  • Step 2: Write down the formula to find the angle in radians (θ). The formula is θ = s / r.
  • Step 3: Substitute the values into the formula. Replace s with 10 cm and r with 5 cm: θ = 10 / 5.
  • Step 4: Perform the division. Calculate 10 divided by 5, which equals 2.
  • Step 5: State the result. The angle in radians subtended by the arc at the center is 2 rad.
  • Arc Length and Central Angle – Understanding the relationship between the arc length, radius, and the angle subtended at the center of a circle.
  • Radians – Knowledge of how angles are measured in radians and the conversion between degrees and radians.
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