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OPRQ is a quadrant of a… (Class 10 Maths Basic 2025, Q25)

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MathsCBSE Class 10 · Basic · Board exam 2025, set 430/3/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic 2025: question 25

Set in the CBSE Class 10 board exam of 2025, paper 430/3/1, section B, question 25, for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q25 · 2 marks · Very short answerAreas Related to Circles

In the given figure, OPRQ is a quadrant of a circle with centre O and radius 10 cm. If OP = 10 cm and OS = 6 cm, find the area of the shaded region. (Use )

Figure in the paper: Quadrant OPRQ of a circle with centre O at bottom right; P is at the left end of the horizontal radius OP (10 cm), Q is at the top of the vertical radius OQ, and R is a point on the arc PQ. S lies on OQ with OS = 6 cm. The shaded region is bounded by the arc PRQ, the segment QS along OQ, and the segment SP. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 430/3/1.

Hints

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

Hint 1

The shaded part is the quadrant with one triangle removed. Which triangle?

Hint 2

Triangle POS is right-angled at O with legs 10 cm and 6 cm.

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 shaded region = Area of quadrant OPRQ − Area of

    1 mark

  2. 1 mark

Answer: 48.5 cm²

Where the marks are

  • Writes shaded area = quadrant − ΔPOS with correct substitution (1 mark)
  • Gets 48.5 cm² (1 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 430/3/1 (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.