MathsCBSE Class 10 · Basic · Board exam 2025, set 430/2/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic 2025: question 25(b)

Set in the CBSE Class 10 board exam of 2025, paper 430/2/1, section B, question 25(b), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q25(b) · 2 marks · Very short answerAreas Related to Circles

In the given figure, O is the centre of a circle of radius 7 cm. AB is a chord of the circle. Find the perimeter of the shaded region.

Figure in the paper: A circle with centre O of radius 7 cm. Chord AB is drawn with OA and OB each marked 7 cm and the angle AOB marked 60 degrees at O. The minor segment between chord AB and the arc is shaded. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 430/2/1.

Hints

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

Hint 1

The shaded segment is bounded by the chord AB and the minor arc AB.

Hint 2

What kind of triangle has two sides equal and the included angle 60°?

Hint 3

Use arc length = (θ/360°) × 2πr.

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.

In $△ A O B$ , $O A = O B = 7$ cm and $∠ A O B = 6 0^{\circ}$ , so the base angles are each $6 0^{\circ}$ and the triangle is equilateral. $∴ A B = 7$ cm.
½ mark
Length of minor arc $A B = \frac{θ}{36 0 ^{\circ}} \times 2 π r = \frac{60}{360} \times 2 \times \frac{22}{7} \times 7 = \frac{22}{3}$ cm.
½ mark
Perimeter of shaded region = arc AB + chord AB $= \frac{22}{3} + 7$ .
½ mark
$= \frac{43}{3}$ cm $\approx 14.33$ cm.
½ mark

Answer: 43/3 cm ≈ 14.33 cm

Where the marks are

Shows AOB equilateral so AB = 7 cm (½ mark)
Arc length = 22/3 cm (½ mark)
Perimeter = arc + chord (½ mark)
Answer 43/3 cm (½ mark)

Revise the chapter

Chapter: Areas Related to Circles (notes, formulas, where marks are lost and every past question)

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 430/2/1 (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 2025: question 25(b)

Hints

Step-by-step solution

Revise the chapter

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