MathsCBSE Class 10 · Standard · Board exam 2026, set 30/1/1 · 4 marks · Case-based

CBSE Class 10 Mathematics Standard 2026: question 38

Set in the CBSE Class 10 board exam of 2026, paper 30/1/1, section E, question 38, for 4 marks. Try it first; the hints and our step-by-step solution are below.

Q38 · 4 marks · Case-basedCompetency-basedAreas Related to Circles

A brooch is crafted from silver wire in the shape of a circle with a diameter of 35 cm. The wire is also used to create 5 diameters, dividing the circle into 10 equal sectors as shown in figure.

Based on the above information, answer the following questions :

(i)
What is the radius of circle ?
1 mark
(ii)
What is the circumference of the brooch ?
1 mark
(iii)(a)
What is the total length of silver wire required ?
2 marks
OR
(iii)(b)
What is the area of each sector of the brooch ?
2 marks

Figure in the paper: A circle divided into 10 equal sectors by 5 diameters, all passing through the centre, giving 10 equal angles at the centre. See it in the official paper.

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

Hints

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

Hint 1

The radius is half the diameter. The circumference is $2 π r$ .

Hint 2

The wire makes the circle and also the 5 diameters.

Hint 3

Ten equal sectors means each central angle is $36 0^{\circ} \div 10$ . Then use $\frac{θ}{36 0 ^{\circ}} π r^{2}$ .

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.

(i) $r = \frac{diameter}{2} = \frac{35}{2} = 17.5 cm$
1 mark
(ii) $Circumference = 2 π r = 2 \times \frac{22}{7} \times \frac{35}{2} = 110 cm$
1 mark
(iii)(a) The wire forms the circle plus 5 diameters, each 35 cm long:
$Total length = 5 \times 35 + 110$
1 mark
(iii)(a) $= 175 + 110 = 285 cm$
1 mark
(iii)(b) The 10 equal sectors share the full angle at the centre:
$Central angle = \frac{36 0 ^{\circ}}{10} = 3 6^{\circ}$
1 mark
(iii)(b) $Area of a sector = \frac{θ}{36 0 ^{\circ}} \times π r^{2} = \frac{36}{360} \times \frac{22}{7} \times \frac{35}{2} \times \frac{35}{2} = \frac{385}{4} = 96.25 cm^{2}$
1 mark

Answer: (i) 17.5 cm; (ii) 110 cm; (iii)(a) 285 cm, (iii)(b) 96.25 cm²

Where the marks are

(i) $r = 17.5$ cm (1 mark)
(ii) Circumference $= 110$ cm (1 mark)
(iii)(a) Writes total length $= 5 \times 35 + 110$ (1 mark)
(iii)(a) Gets 285 cm (1 mark)
(iii)(b) Central angle $= 3 6^{\circ}$ (1 mark)
(iii)(b) Sector area $= 96.25$ cm² (1 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 30/1/1 (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 38

Hints

Step-by-step solution

Revise the chapter

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