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The area of a smaller… (Class 10 Maths Basic 2025, Q25a)

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

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

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

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

The area of a smaller circle is equal to the area of a sector of a larger circle with central angle . The radii of the smaller and larger circles are 'r' and 'R' respectively. Find r : R.

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

Area of a sector of angle θ is (θ/360°) × πR².

Hint 2

Equate the two areas and cancel π, then take square roots.

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.

  1. Area of smaller circle = area of sector of larger circle: .

    1 mark

  2. .

    ½ mark

  3. , so .

    ½ mark

Answer: r : R = 1 : √3

Where the marks are

  • Forms the equation (1 mark)
  • Gets (½ mark)
  • Gets (½ mark)

Revise the chapter

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.