MathsCBSE Class 10 · Basic · Board exam 2023, set 430/2/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Basic 2023: question 26

Set in the CBSE Class 10 board exam of 2023, paper 430/2/1, section C, question 26, for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q26 · 3 marks · Short answerAreas Related to Circles

In the given figure, two concentric circles with centre O are shown. Radii of the circles are 2 cm and 5 cm respectively. Find the area of the shaded region.

Figure in the paper: Two concentric circles with centre O; inner radius 2 cm, outer radius 5 cm. Two radii OA and OC go to the outer circle and OE and OD to the inner circle, with $∠$ EOD = $6 0^{\circ}$ marked at O. The shaded region is bounded by segment EA, arc AC of the outer circle (through B), segment CD and arc ED of the inner circle. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 430/2/1.

Hints

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

Hint 1

The shaded part is a big sector with a smaller sector cut out, both with angle 60°.

Hint 2

Use area of sector $= \frac{θ}{36 0 ^{\circ}} π r^{2}$ for r = 5 and r = 2, then subtract.

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 sector OAC of the outer circle (r = 5 cm, θ = 60°) $= \frac{6 0 ^{\circ}}{36 0 ^{\circ}} \times π \times 5^{2} = \frac{25 π}{6} cm^{2}$
1 mark
Area of sector OED of the inner circle (r = 2 cm, θ = 60°) $= \frac{6 0 ^{\circ}}{36 0 ^{\circ}} \times π \times 2^{2} = \frac{4 π}{6} cm^{2}$
1 mark
Area of shaded region $= \frac{25 π}{6} - \frac{4 π}{6} = \frac{21 π}{6} = \frac{21}{6} \times \frac{22}{7} = 11 cm^{2}$
1 mark

Answer: 11 cm²

Where the marks are

Area of outer sector $\frac{25 π}{6}$ cm² (1 mark)
Area of inner sector $\frac{4 π}{6}$ cm² (1 mark)
Shaded area = difference = 11 cm² (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 paper2023 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.

CBSE Class 10 Mathematics Basic 2023: question 26

Hints

Step-by-step solution

Revise the chapter

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