Question 141 markMCQSection A

  1. The length of the arc of the sector of a circle with radius 21 cm and of central angle 60°, is : (a) 22 cm (b) 44 cm (c) 88 cm (d) 11 cm

Areas Related to Circles
Length of an arc

Options

(A)22 cm
(B)44 cm
(C)88 cm
(D)11 cm

Official answer

(a) 22 cm, obtained from arc length = (60/360)×2×(22/7)×21=22 cm(60/360) \times 2 \times (22/7) \times 21 = 22 \text{ cm}.

Answer keywords:arc lengthsectorcentral angleθ/3602πrπ = 22/7circumference22 cm

Marking scheme

  1. 1.1 mark for correct option (a) 22 cm.
  2. 2.Expected working: arc = (60/360)×2×(22/7)×21=(1/6)×132=22 cm(60/360) \times 2 \times (22/7) \times 21 = (1/6) \times 132 = 22 \text{ cm}.
  3. 3.Accept the answer if the correct arc-length formula and π=227\pi = \frac{22}{7} are used.

Hint

Arc length = (θ/360)×2πr(\theta/360) \times 2\pi r. Here θ/360=60/360=1/6\theta/360 = 60/360 = 1/6 of the circumference.

Quick oral answer

Arc length equals theta over 360 times 2 pi r; with 60 degrees, radius 21 and pi as 22 by 7, that is one-sixth of 132, which is 22 centimetres.

Common mistakes

  1. 1.Using the sector area formula (θ/360×πr2)(\theta/360 \times \pi r^2) instead of the arc length formula, giving 231 cm2231 \text{ cm}^2 and confusion.
  2. 2.Dropping the factor 2 in 2πr2\pi r and getting 11 cm (option d).
  3. 3.Miscomputing 60/36060/360 as 1/31/3 instead of 1/61/6, doubling the answer to 44 cm.

Analysis and explanation

Tests the direct application of the arc-length formula for a sector using the given radius and central angle.


Concept

  • Arc length of a sector = (θ360°)×2πr\left(\frac{\theta}{360°}\right) \times 2\pi r, where θ is the central angle and r is the radius.
  • Here θ=60°\theta = 60°, r=21 cmr = 21 \text{ cm}, and π=227\pi = \frac{22}{7} (chosen because 21 is a multiple of 7, simplifying the calculation).

Key points

  • Substituting gives (60360)×2×(227)×21=(16)×132=22 cm\left(\frac{60}{360}\right) \times 2 \times \left(\frac{22}{7}\right) \times 21 = \left(\frac{1}{6}\right) \times 132 = 22 \text{ cm}.

Common mistakes

  • Confusing arc length with sector area (which would involve r² instead of r).
  • Using π = 3.14 instead of 22/7, which needlessly complicates a problem designed for exact cancellation.

Interesting facts

For any circle, a 60° sector always contains exactly one-sixth of the circumference and one-sixth of the area — the same reason a regular hexagon fits perfectly inside a circle.

Radius 21 cm is a favourite CBSE choice because 21 is a multiple of 7, making π=227\pi = \frac{22}{7} cancel cleanly and giving whole-number answers.

Question details

Q14 of 53 questions

Board
CBSE
Class
Class 10
Subject
Mathematics (Basic)
Year
2026
Section
Section A
Marks
1
Type
MCQ
Chapter
Areas Related to Circles
Topic
Length of an arc
Bloom's level
apply
Syllabus topic
Unit 5: Mensuration — Areas Related to Circles: Length of an arc of a sector
Author
CBSE
Reviewed by
Padhantu Academic Team

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Frequently asked questions

What is the formula for the length of an arc?

Arc length = (θ/360°)×2πr(\theta/360°) \times 2\pi r, where θ is the central angle and r is the radius. It is the corresponding fraction of the full circumference 2πr.

Why do we use π = 22/7 here?

Because the radius 21 is a multiple of 7, using 227\frac{22}{7} cancels neatly to give a whole-number answer. The question implicitly expects this standard value.

How is arc length different from sector area?

Arc length is a distance measured in cm along the boundary, using 2πr2\pi r; sector area is a region measured in cm² using πr2\pi r^2. Mixing them is a common error.