MathsCBSE Class 10 · Standard · Sample paper, session 2025-26 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard sample paper 2025-26: question 7

From the official CBSE sample question paper for 2025-26, section A, question 7, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q7 · 1 mark · MCQCompetency-basedAreas Related to Circles

Given below is the picture of the Olympic rings made by taking five congruent circles of radius 1cm each, intersecting in such a way that the chord formed by joining the point of intersection of two circles is also of length 1cm. Total area of all the dotted regions (assuming the thickness of the rings to be negligible) is

For Visually Impaired candidates: The area of the circle that can be inscribed in a square of 6 cm is (A) $36 π$ cm $^{2}$ (B) $18 π$ cm $^{2}$ (C) $12 π$ cm $^{2}$ (D) $9 π$ cm $^{2}$

(A) $4 [\frac{π}{12} - \frac{3}{4}]$ cm $^{2}$
(B) $[\frac{π}{6} - \frac{3}{4}]$ cm $^{2}$
(C) $4 [\frac{π}{6} - \frac{3}{4}]$ cm $^{2}$
(D) $8 [\frac{π}{6} - \frac{3}{4}]$ cm $^{2}$

Figure in the paper: Five interlocking Olympic rings (three on top row: blue, black, red; two below: yellow, green). Adjacent rings intersect; the lens-shaped overlapping regions are dotted. Points A and B are marked at the intersection points of the blue and yellow rings, with chord AB drawn. See it in the official paper.

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2025-26.

Hints

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

Hint 1

A chord equal to the radius makes an equilateral triangle with the centre.

Hint 2

Count how many lens-shaped overlaps there are; each lens is two segments.

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.

Adjacent rings overlap in 4 places (blue–yellow, yellow–black, black–green, green–red). Each lens-shaped overlap is made of 2 circular segments, so there are 8 segments in all.
The chord AB = 1 cm equals the radius. So triangle OAB is equilateral and the central angle is $6 0^{\circ}$ .
Area of one segment $= \frac{6 0 ^{\circ}}{36 0 ^{\circ}} π (1)^{2} - \frac{3}{4} (1)^{2} = \frac{π}{6} - \frac{3}{4}$ . Total area $= 8 [\frac{π}{6} - \frac{3}{4}]$ cm $^{2}$ , which is option (D).
1 mark
For Visually Impaired candidates: the circle inscribed in a square of side 6 cm has radius 3 cm. Its area is $π (3)^{2} = 9 π$ cm $^{2}$ , which is option (D).

Answer: $8 [\frac{π}{6} - \frac{3}{4}]$ cm², option (D) (VI: 9π cm², option (D))

Where the marks are

Finds the 60° segment area, multiplies by 8 segments and selects option (D) (1 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 paperSample paper 2025-26 (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 sample paper 2025-26: question 7

Hints

Step-by-step solution

Revise the chapter

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