In the given figure, three sectors of a circle of radius 5 cm, making angles 35°, 50° and 95° at the centre are shaded. Find the area of the shaded region. [Use π = 22/7]

MathsCBSE Class 10 · Standard · Board exam 2025, set 30/2/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Standard 2025: question 22(b)

Set in the CBSE Class 10 board exam of 2025, paper 30/2/1, section B, question 22(b), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q22(b) · 2 marks · Very short answerAreas Related to Circles

In the given figure, three sectors of a circle of radius 5 cm, making angles $3 5^{\circ}$ , $5 0^{\circ}$ and $9 5^{\circ}$ at the centre are shaded. Find the area of the shaded region. [Use $π = \frac{22}{7}$ ]

Figure in the paper: A circle of radius 5 cm divided by radii into sectors. Three sectors are shaded: one labelled $9 5^{\circ}$ at the upper-left, one labelled $5 0^{\circ}$ at the right-lower side, and one labelled $3 5^{\circ}$ at the lower-left. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 30/2/1.

Hints

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

Hint 1

The area of a sector is $\frac{θ}{360} \times π r^{2}$ .

Hint 2

All three sectors have the same radius, so you can add their angles first.

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.

Shaded area $= \frac{95}{360} π r^{2} + \frac{50}{360} π r^{2} + \frac{35}{360} π r^{2}$ , with $r = 5$ cm.
1 mark
$= \frac{95 + 50 + 35}{360} \times \frac{22}{7} \times 5^{2} = \frac{180}{360} \times \frac{22}{7} \times 25$ .
½ mark
$= \frac{275}{7}$ cm $^{2} \approx 39.29$ cm $^{2}$ .
½ mark

Answer: $\frac{275}{7}$ cm² ≈ 39.29 cm²

Where the marks are

Writes the sum of the three sector areas using $\frac{θ}{360} π r^{2}$ (1 mark)
Combines the angles to $18 0^{\circ}$ (½ mark)
Gets $\frac{275}{7}$ 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 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 paper2025 board paper, set 30/2/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2025: question 22(b)

Hints

Step-by-step solution

Revise the chapter

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