MathsCBSE Class 10 · Standard · Board exam 2026, set 30/5/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Standard 2026: question 26

Set in the CBSE Class 10 board exam of 2026, paper 30/5/1, section C, question 26, for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q26 · 3 marks · Short answerAreas Related to Circles

A circle of diameter 20 cm is equally divided into five sectors. Find the area and perimeter of one of the sectors.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 30/5/1.

Hints

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

Hint 1

Five equal sectors share the full $36 0^{\circ}$ equally.

Hint 2

Area of sector $= \frac{θ}{360} π r^{2}$ ; arc length $= \frac{θ}{360} 2 π r$ .

Hint 3

Perimeter of a sector includes the two radii as well as the arc.

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. Central angle of each sector $θ = \frac{36 0 ^{\circ}}{5} = 7 2^{\circ}$ .
½ mark
Area of one sector $= \frac{θ}{36 0 ^{\circ}} \times π r^{2} = \frac{72}{360} \times \frac{22}{7} \times 10 \times 10$
½ mark
$= \frac{440}{7}$ cm² $\approx 62.86$ cm²
½ mark
Perimeter of sector $=$ arc length $+ 2 r = \frac{72}{360} \times 2 \times \frac{22}{7} \times 10 + 10 + 10 = \frac{88}{7} + 20$
1 mark
$= \frac{228}{7}$ cm $\approx 32.57$ cm
½ mark

Answer: Area $= \frac{440}{7}$ cm² ≈ 62.86 cm²; Perimeter $= \frac{228}{7}$ cm ≈ 32.57 cm

Where the marks are

Radius 10 cm and central angle $7 2^{\circ}$ (½ mark)
Correct area formula with substitution (½ mark)
Area $= \frac{440}{7}$ cm² (½ mark)
Perimeter = arc length + 2r with substitution (1 mark)
Perimeter $= \frac{228}{7}$ cm (½ mark)

Revise the chapter

Chapter: Areas Related to Circles (notes, formulas, where marks are lost and every past question)
Topic: Area of a Sector 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 30/5/1 (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 26

Hints

Step-by-step solution

Revise the chapter

More questions from Areas Related to Circles