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Mathematics

Arc length

In this Class 9 Mathematics topic from the chapter Area and Perimeter, students learn how to find the length of a curved part of a circle, called an arc. They connect arc length with the circumference and central angle, use the appropriate fraction of 360°, and apply the formula in routine problems. The topic also develops accurate use of radius, diameter, π, units, and step-by-step reasoning for measuring curved boundaries in figures and everyday situations.

Medium · Level 1 · 1 questions

Practice questions

01A sector has perimeter 32 cm and arc length 12 cm. What is its central angle in radians?

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Answer and explanation

Correct answer: B. 6/5

Use the sector-perimeter formula P = 2r + s, because the boundary contains two radii and one arc. With P = 32 cm and s = 12 cm, we obtain 32 = 2r + 12. Thus 2r = 20 and r = 10 cm. In radian measure, arc length satisfies s = rθ, so θ = s/r = 12/10 = 6/5 radians. Therefore option B is correct. The fraction 5/6 reverses the required ratio and would correspond to r/s rather than s/r. The other choices are not supported by either the perimeter equation or the arc-length formula. Substitution also checks the result: 10 × 6/5 = 12 and 2(10) + 12 = 32.

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Arc length

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