In the given figure, the shape of the top of a table is that of a sector of a circle with centre O and ∠ AOB = 90°. If AO = OB = 42 cm, then find the perimeter of the top of the table.

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

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

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

Q22(a) · 2 marks · Very short answerCompetency-basedAreas Related to Circles

In the given figure, the shape of the top of a table is that of a sector of a circle with centre O and $∠ A O B = 9 0^{\circ}$ . If $A O = O B = 42$ cm, then find the perimeter of the top of the table.

Figure in the paper: A major sector of a circle with centre O. Radii OA and OB form a right angle at O (marked with a square). A is at the lower-left and B at the lower-right; the large arc AB runs over the top. The sector is the reflex-angled shape of the table top. 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 table top is the larger sector, so its angle is not $9 0^{\circ}$ .

Hint 2

Perimeter of a sector $=$ arc length $+$ two radii, with arc length $\frac{θ}{360} \times 2 π r$ .

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.

The table top is the major sector. Its angle is reflex $∠ A O B = 36 0^{\circ} - 9 0^{\circ} = 27 0^{\circ}$ .
½ mark
Perimeter $=$ length of major arc $+ 2 r = \frac{270}{360} \times 2 \times \frac{22}{7} \times 42 + 2 \times 42 = 198 + 84$ .
1 mark
Perimeter $= 282$ cm.
½ mark

Answer: 282 cm

Where the marks are

Finds the reflex angle as $27 0^{\circ}$ (½ mark)
Uses perimeter $=$ arc length $\frac{θ}{360} \times 2 π r$ plus $2 r$ with correct substitution (1 mark)
Gets 282 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 30/2/1 (Standard): every question, by section.

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

Hints

Step-by-step solution

Revise the chapter

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