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Mathematics — CBSE Class 10 board question

Q1. [1]
If an arc subtends an angle of 90° at the centre of a circle, then the ratio of its length to the circumference of the circle is :
  1. A 2 : 3
  2. B 1 : 4
  3. C 4 : 1
  4. D 1 : 3
Previously asked in CBSE board exam
2024 30/4/1 Q5
Generated by claude-sonnet-4-6 · 2026-06-15 10:37 · grounding rag
Model Answer

Option B: 1 : 4

Arc length = $\dfrac{90}{360} \times 2\pi r = \dfrac{1}{4} \times 2\pi r$. Ratio of arc length to circumference $= \dfrac{\frac{1}{4} \times 2\pi r}{2\pi r} = \dfrac{1}{4}$, i.e., 1 : 4.

Explanation

The arc length formula $\dfrac{\theta}{360} \times 2\pi r$ gives the arc as a fraction of the full circumference $2\pi r$. With $\theta = 90°$, that fraction is $\frac{90}{360} = \frac{1}{4}$, directly giving the ratio 1 : 4. Always cancel $2\pi r$ to find the ratio quickly.

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