This 2019 CBSE class 10 Maths 3 mark question is from Areas Related to Circles. This 3-mark question tests concept of computing area of a segment of a Circle. From the chapter Areas Related to Circles.

Question 20: Find the area of the minor segment of a circle of radius 42 cm, if length of the corresponding arc is 44 cm.

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**Area of the minor segment ADB = Area of sector OADB – Area of ΔOAB**

Length of the arc of the minor segment = 44 cm

Length of arc that subtends an angle θ = \\frac{θ}{360}) × 2πr

\\frac{θ}{360}) × 2πr = \\frac{θ}{360}) × 2 × \\frac{22}{7}) × 42 = 44

θ = \\frac{44 × 7 × 360}{2 × 22 × 42}) = 60°

Area of Sector = \\frac{θ}{360}) × πr^{2}

= \\frac{60}{360}) × \\frac{22}{7}) × 42 × 42

= 924 cm^{2}

OA = OB. So, ∠OAB = ∠OBA. Let ∠OBA = x

∠AOB = 60°

In a triangle sum of interior angles = 180°

60 + x + x = 180. Or x = 60°

So, ∠OAB is an equilateral triangle.

Area of ∠OAB = \\frac{√3}{4}) × a^{2}, where 'a' is the side of the triangle

Area of ∠OAB = \\frac{√3}{4}) × 42 × 42 = 441√3

Area of the minor segment ADB = Area of sector OADB – Area of ΔOAB

= 924 - 441√3

= **21 (44 - 21√3) cm ^{2}**

Class 10 Maths

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CBSE Class 10 Maths - 2021

- Real Numbers Revision Class
- Polynomials Revision Videos
- Linear Equations Revision Class
- Quadratic Equations Revision Class
- Arithmetic Progressions Revision Video
- Triangles Revision
- Coordinate Geometry Revision
- Trigonometry Revision Class
- Appl of Trigonometry
- Circles Revision Class
- Areas Related to Circles Revision Videos

1. Section A | 2018 CBSE Class 10 Maths 1 Mark **Questions 1 to 2** ▶

2. Section A | 2019 CBSE Class 10 Maths 1 Mark **Question 3 to 4** ▶

3. Section A | 2019 CBSE Class 10 Maths 1 Mark **Question 5 to 6** ▶

4. Section B | 2019 CBSE Class 10 Maths 2 Mark **Question 7** | Real Numbers ▶

5. Section B | 2019 CBSE Class 10 Maths 2 Mark **Question 8** | Arithmetic Progressions ▶

6. Section B | 2019 CBSE Class 10 Maths 2 Mark **Question 9** | Coordinate Geometry ▶

7. Section B | 2019 CBSE Class 10 Maths 2 Mark **Question 10** | Probability ▶

8. Section B | 2019 CBSE Class 10 Maths 3 Mark **Question 11** | Probability ▶

9. Section B | 2019 CBSE Class 10 Maths 3 Mark **Question 12** | Linear Equations ▶

10. Section C | 2019 CBSE Class 10 Maths 3 Mark **Question 13** | Real Numbers & HCF ▶

11. Section C | 2019 CBSE Class 10 Maths 3 Mark **Question 14** | Polynomials ▶

12. Section C | 2019 CBSE Class 10 Maths 3 Mark **Question 15** | Linear Equations ▶

13. Section C | 2019 CBSE Class 10 Maths 3 Mark **Question 16** | Coordinate Geometry ▶

14. Section C | 2019 CBSE Class 10 Maths 3 Mark **Question 17** | Trigonometric Ratios ▶

15. Section C | 2019 CBSE Class 10 Maths 3 Mark **Question 18** | Circles ▶

16. Section C | 2019 CBSE Class 10 Maths 3 Mark **Question 19** | Triangles ▶

17. Section C | 2019 CBSE Class 10 Maths 3 Mark **Question 20** | Areas Related to Circles ▶

18. Section C | 2019 CBSE Class 10 Maths 3 Mark **Question 21** | Statistics - Median ▶

19. Section C | 2019 CBSE Class 10 Maths 3 Mark **Question 22** | Statistics ▶

20. Section D | 2019 CBSE Class 10 Maths 4 Mark **Question 23** | Quadratic Equations ▶

21. Section D | 2019 CBSE Class 10 Maths 4 Mark **Question 24** | Arithmetic Progressions ▶

22. Section D | 2019 CBSE Class 10 Maths 4 Mark **Question 25** | Triangles ▶

23. Section D | 2019 CBSE Class 10 Maths 4 Mark **Question 27** | Trigonometry ▶

24. Section D | 2019 CBSE Class 10 Maths 4 Mark **Question 28** | Statistics ▶

25. Section D | 2019 CBSE Class 10 Maths 4 Mark **Question 29** | Surface Areas ▶

26. Section D | 2019 CBSE Class 10 Maths 4 Mark **Question 30** | Trigonometry ▶

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