MathsCBSE Class 10 · Basic · Board exam 2026, set 430/1/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic 2026: question 25

Set in the CBSE Class 10 board exam of 2026, paper 430/1/1, section B, question 25, for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q25 · 2 marks · Very short answerAreas Related to Circles

A chord of a circle of diameter 20 cm subtends an angle of $6 0^{\circ}$ at the centre of the circle. Find the area of the corresponding minor segment of the circle. (Use $π = 3 \cdot 14$ and $3 = 1 \cdot 73$ )

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 430/1/1.

Hints

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

Hint 1

Minor segment = sector − triangle formed by the two radii and the chord.

Hint 2

Radius is half the diameter. Use $\frac{θ}{360} π r^{2}$ for the sector.

Hint 3

With a 60° angle between two equal radii, the triangle is equilateral, so its area is $\frac{3}{4} r^{2}$ .

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.

Radius $r = \frac{20}{2} = 10$ cm, $θ = 6 0^{\circ}$ . Area of sector $= \frac{60}{360} \times 3.14 \times 1 0^{2} = \frac{314}{6} \approx 52.33$ cm².
½ mark
The two radii are equal and the included angle is $6 0^{\circ}$ , so the triangle is equilateral with side 10 cm. Area of triangle $= \frac{3}{4} \times 1 0^{2} = \frac{1.73 \times 100}{4} = 43.25$ cm².
1 mark
Area of minor segment $=$ area of sector $-$ area of triangle $= 52.33 - 43.25 = 9.08$ cm² (approx.).
½ mark

Answer: Area of minor segment ≈ 9.08 cm²

Where the marks are

Area of sector ≈ 52.33 cm² (½ mark)
Area of equilateral triangle = 43.25 cm² (1 mark)
Area of segment ≈ 9.08 cm² (½ 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 430/1/1 (Basic): 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 Basic 2026: question 25

Hints

Step-by-step solution

Revise the chapter

More questions from Areas Related to Circles