Area of a segment of a circle of radius 'r' and central angle 60° is : (A) (π r²)/(2) - 1/2r² (B) (2π r)/(4) - (√(3))/(4)r² (C) (π r²)/(6) - (√(3))/(4)r² (D) (2π r)/(4) - r² 60°

MathsCBSE Class 10 · Standard · Board exam 2026, set 30/2/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard 2026: question 15

Set in the CBSE Class 10 board exam of 2026, paper 30/2/1, section A, question 15, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q15 · 1 mark · MCQAreas Related to Circles

Area of a segment of a circle of radius 'r' and central angle $6 0^{\circ}$ is :

(A) $\frac{π r ^{2}}{2} - \frac{1}{2} r^{2}$
(B) $\frac{2 π r}{4} - \frac{3}{4} r^{2}$
(C) $\frac{π r ^{2}}{6} - \frac{3}{4} r^{2}$
(D) $\frac{2 π r}{4} - r^{2} sin 6 0^{\circ}$

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 30/2/1.

Hints

Open one hint at a time and try again before the next.

Hint 1

Segment = sector − triangle.

Hint 2

With 60° the triangle is equilateral.

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

Sector = $\frac{60}{360} π r^{2} = \frac{π r ^{2}}{6}$ ; triangle is equilateral with area $\frac{3}{4} r^{2}$ .
Segment = $\frac{π r ^{2}}{6} - \frac{3}{4} r^{2}$ . Option (C).
1 mark

Answer: Option (C)

Where the marks are

Sector minus equilateral triangle area (1 mark)

Revise the chapter

Chapter: Areas Related to Circles (notes, formulas, where marks are lost and every past question)
Topic: Area of a Segment of a Circle

Practise this chapterBoard-style questions from Areas Related to Circles, one at a time, marked against the answer key and marking points.Back to the full paper2026 board paper, set 30/2/1 (Standard): every question, by section.

The question is transcribed from the official paper; figures are described in words. The solution, hints and chapter tag are ours. Spotted an error? Write tosupport@questionbuddy.in.

CBSE Class 10 Mathematics Standard 2026: question 15

Hints

Step-by-step solution

Revise the chapter

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