MathsCBSE Class 10 · Basic · Board exam 2026, set 430/4/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Basic 2026: question 27

Set in the CBSE Class 10 board exam of 2026, paper 430/4/1, section C, question 27, for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q27 · 3 marks · Short answerAreas Related to Circles

A chord of a circle of radius $14$ cm subtends a right angle at the centre. Find the area of the corresponding (i) minor segment (ii) major segment.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 430/4/1.

Hints

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

Hint 1

A segment is a sector minus the triangle formed by the two radii and the chord.

Hint 2

With a right angle at the centre, the triangle's area is $\frac{1}{2} r^{2}$ .

Hint 3

The major segment is what remains of the whole circle after removing the minor segment.

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.

(i) Area of minor segment = area of sector − area of right triangle $= \frac{90}{360} \times \frac{22}{7} \times 14 \times 14 - \frac{1}{2} \times 14 \times 14$
1 mark
$= 154 - 98 = 56 cm^{2}$
1 mark
(ii) Area of major segment = area of circle − minor segment $= \frac{22}{7} \times 14 \times 14 - 56$
½ mark
$= 616 - 56 = 560 cm^{2}$
½ mark

Answer: (i) 56 cm²; (ii) 560 cm²

Where the marks are

Correct expression sector − triangle for minor segment (1 mark)
Minor segment $= 56$ cm² (1 mark)
Major segment = circle − minor segment (½ mark)
Major segment $= 560$ 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 430/4/1 (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 27

Hints

Step-by-step solution

Revise the chapter

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