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Question

What is the central angle of a sector with an arc length of 10 cm in a circle of radius 5 cm?

This question was previously asked in
SSC CGL 2025 Tier 2 Paper 1 Question Paper (19-Jan-2026)
The correct answer is

2 radians

Arc-length formula: \(s = r\theta\), where \(\theta\) is the central angle in radians.

\(\theta = \dfrac{s}{r} = \dfrac{10}{5} = 2\) radians.

Hence, the central angle is 2 radians.

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Similar Questions

  1. The angle subtended by an arc at the center is $72^\circ$, and its length is $22\text{ cm}$. Find the radius of the circle.
  2. If an angle θ=2 radians, what percentage of the full circle does it represent?

  3. A sector of radius 14 cm has an area of $154 \text{ cm}^2$. Find the angle of the sector.
  4. In a circle of radius r, a chord subtends an angle $\theta$ (in radians) at the center. Which expression represents the length of the minor arc?
  5. An angle of $\frac{\pi}{2}$ radians represents what percentage of a full circle?

Important Questions from Circular Measure of Angles

  1. Which of the following values of A and B satisfies, sin(A + B) = sin A + sin B, where

  2. If tan 3 θ = cot(θ - 22°), where 3 θ is an angle, find the value of θ.

  3. The value of 4cos\(\left( {\frac{\pi }{6}\, - \,\alpha } \right)\) sin\(\left( {\frac{\pi }{3}\, - \,\alpha } \right)\) is equal to:

  4. 1 + tan 15° cot 75° is equal to:

  5. If tan θ = 1/√5, find the value of cosec2θ – sec2θ.

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