AB is a chord of a circle centred at O such that ∠ AOB = 60°. If OA = 14 cm then find the area of the minor segment. (take √(3)=1.73)

MathsCBSE Class 10 · Standard · Sample paper, session 2024-25 · 3 marks · Short answer

CBSE Class 10 Mathematics Standard sample paper 2024-25: question 30(B)

From the official CBSE sample question paper for 2024-25, section C, question 30(B), for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q30(B) · 3 marks · Short answerAreas Related to Circles

$A B$ is a chord of a circle centred at $O$ such that $∠ A O B = 6 0^{\circ}$ . If $O A = 14$ cm then find the area of the minor segment. (take $3 = 1.73$ )

Figure in the paper: A circle with centre O at the top. A and B are two points on the circle at the bottom, with chord AB joined. OA and OB are radii forming the angle AOB at the centre. See it in the official paper.

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2024-25.

Hints

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

Hint 1

Minor segment = sector − triangle.

Hint 2

With two equal radii and a $6 0^{\circ}$ angle between them, $△ O A B$ is equilateral, so use $\frac{3}{4} a^{2}$ .

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.

Area of the minor segment = area of sector $O A B$ − area of $△ O A B$ .
Area of sector $O A B = \frac{60}{360} \times \frac{22}{7} \times 14 \times 14 = \frac{1}{6} \times 616 \approx 102.67 cm^{2}$
1 mark
$O A = O B$ (radii) and $∠ A O B = 6 0^{\circ}$ , so $△ O A B$ is equilateral with side 14 cm.
Area $= \frac{3}{4} \times 1 4^{2} = 493 = 49 \times 1.73 = 84.77 cm^{2}$
1 mark
Area of the minor segment $= 102.67 - 84.77 \approx 17.90 cm^{2}$
1 mark

Answer: $\approx 17.9 cm^{2}$ (17.90 cm²)

Where the marks are

Finds the area of the sector, $\approx 102.67 cm^{2}$ (1 mark)
Finds the area of equilateral $△ O A B$ , $84.77 cm^{2}$ (1 mark)
Subtracts to get the segment area $\approx 17.9 cm^{2}$ (1 mark)

Revise the chapter

Chapter: Areas Related to Circles (notes, formulas, where marks are lost and every past question)
Topic: Area of a Segment of a Circle

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 2024-25 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard sample paper 2024-25: question 30(B)

Hints

Step-by-step solution

Revise the chapter

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