Understanding Areas Related to Circles helps students learn how to calculate the areas of circular regions, sectors, and segments using the correct mathematical formulas. The chapter also covers arc lengths, circumferences, and shaded areas, helping students develop calculation accuracy and problem solving skills. Practicing MCQs helps students to test their understanding and prepare for objective questions in CBSE board exams.
A strong understanding of these concepts helps students solve application-based questions with greater confidence. Students can also explore CBSE Board resources and MCQs Class 10 Maths to strengthen their preparation according to the latest syllabus.
Topics Covered
Before solving Areas Related to Circles Class 10 MCQs with Answers, students should revise all important formulas and concepts carefully because most questions are directly formula and figure based. Important concepts covered in this chapter include:
- Area of circle
- Circumference of circle
- Radius and diameter
- Sector of circle
- Segment of circle
- Arc length
- Semicircle
- Quadrant
- Central angle
- Shaded region calculations
- Circle-based mensuration formulas
- Curved boundary measurements
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Class 10 Maths Chapter 11 MCQs with Answers and Explanations
Practise Areas Related to Circles questions to improve your Maths preparation and revise important formulas. These objective questions help students improve formula application, mensuration calculations, figure analysis, and board exam preparation skills effectively.
Q1. The circumference of a circle is 88 cm. Find its radius. A) 12 cm B) 14 cm C) 16 cm D) 18 cm
Answer: B Explanation: Circumference = 2pi r 88 = 2 x (22/7) x r 88 = (44/7)r r = 14 cm.
Q2. Find the area of a sector of a circle with radius 14 cm and central angle 60 degree.
- A) 154 sq cm
- B) 308/3 sq cm
- C) 616/3 sq cm
- D) 462 sq cm
Answer: B Explanation: Area of sector = (theta/360) x pi r^2 = (60/360) x (22/7) x 14 x 14 = 308/3 sq cm.
Q3. A wheel has radius 35 cm. How much distance will it cover in 20 revolutions?
- A) 22 m
- B) 44 m
- C) 66 m
- D) 88 m
Answer: B Explanation: Distance in one revolution = circumference = 2 x (22/7) x 35 = 220 cm Distance in 20 revolutions = 220 x 20 = 4400 cm = 44 m.
Q4. Find the length of an arc subtending an angle 90 degree at the center of a circle of radius 21 cm.
- A) 22 cm
- B) 33 cm
- C) 44 cm
- D) 66 cm
Answer: B Explanation: Arc length = (90/360) x 2pi r = (1/4) x 2 x (22/7) x 21 = 33 cm.
Q5. The area of a circle is 616 sq cm. Find its radius.
- A) 7 cm
- B) 14 cm
- C) 21 cm
- D) 28 cm
Answer: B Explanation: Area = pi r^2 616 = (22/7)r^2 r^2 = 196 r = 14 cm.
Q6. Find the area of a quadrant of radius 10 cm.
- A) 25pi sq cm
- B) 50pi sq cm
- C) 75pi sq cm
- D) 100pi sq cm
Answer: A Explanation: Area of quadrant = (1/4)pi r^2 = (1/4)pi x 10^2 = 25pi sq cm.
Q7. The diameter of a circle is 28 cm. Find its circumference.
- A) 44 cm
- B) 66 cm
- C) 88 cm
- D) 176 cm
Answer: C Explanation: Circumference = pi d = (22/7) x 28 = 88 cm.
Q8. A sector has radius 7 cm and angle 180 degree. Find its area.
- A) 49pi sq cm
- B) 77 sq cm
- C) 154 sq cm
- D) 98 sq cm
Answer: B Explanation: Area of sector = (180/360) x pi x 7^2 = (1/2) x (22/7) x 49 = 77 sq cm.
Q9. Find the area of a circle whose circumference is 44 cm.
- A) 154 sq cm
- B) 308 sq cm
- C) 616 sq cm
- D) 77 sq cm
Answer: A Explanation: 2pi r = 44 2 x (22/7) x r = 44 r = 7 cm Area = (22/7) x 7 x 7 = 154 sq cm.
Q10. A minute hand of length 14 cm sweeps through 30 degree. Find the area swept.
- A) 154/3 sq cm
- B) 77/3 sq cm
- C) 44 sq cm
- D) 88 sq cm
Answer: A Explanation: Area swept = (30/360) x pi x 14^2 = (1/12) x (22/7) x 196 = 154/3 sq cm.
Q11. Find the area of a semicircle of radius 21 cm.
- A) 693 sq cm
- B) 1386 sq cm
- C) 346.5 sq cm
- D) 231 sq cm
Answer: A Explanation: Area of semicircle = (1/2)pi r^2 = (1/2) x (22/7) x 21 x 21 = 693 sq cm.
Q12. The radius of a circle is increased from 7 cm to 14 cm. The area becomes:
- A) Double
- B) Triple
- C) Four times
- D) Eight times
Answer: C Explanation: Area depends on r^2. If radius doubles, area becomes 2^2 = 4 times.
Q13. Find the perimeter of a semicircle of radius 14 cm.
- A) 44 cm
- B) 72 cm
- C) 88 cm
- D) 66 cm
Answer: B Explanation: Perimeter of semicircle = pi r + 2r = (22/7) x 14 + 28 = 44 + 28 = 72 cm.
Q14. The area of a circle is numerically equal to its circumference. Find the radius.
- A) 1 unit
- B) 2 units
- C) 3 units
- D) 4 units
Answer: B Explanation: pi r^2 = 2pi r r = 2 units.
Q15. A wire of length 88 cm is bent into the shape of a circle. Find its radius.
- A) 7 cm
- B) 14 cm
- C) 21 cm
- D) 28 cm
Answer: B Explanation: Circumference = 88 cm 2 x (22/7) x r = 88 r = 14 cm.
Q16. Find the length of the arc of a sector with angle 120 degree and radius 14 cm.
- A) 88/3 cm
- B) 44/3 cm
- C) 66 cm
- D) 22 cm
Answer: A Explanation: Arc length = (120/360) x 2pi r = (1/3) x 2 x (22/7) x 14 = 88/3 cm.
Q17. The area of a circle inscribed in a square of side 14 cm is:
- A) 49pi sq cm
- B) 98pi sq cm
- C) 154 sq cm
- D) 196 sq cm
Answer: A Explanation: Diameter = side = 14 cm Radius = 7 cm Area = pi x 7^2 = 49pi sq cm.
Q18. A circle has radius 10.5 cm. Find its circumference.
- A) 44 cm
- B) 55 cm
- C) 66 cm
- D) 77 cm
Answer: C Explanation: Circumference = 2pi r = 2 x (22/7) x 10.5 = 66 cm.
Q19. Find the area of the ring formed by two concentric circles of radii 14 cm and 7 cm.
- A) 462 sq cm
- B) 308 sq cm
- C) 154 sq cm
- D) 616 sq cm
Answer: A Explanation: Area of ring = pi(R^2 - r^2) = (22/7)(196 - 49) = (22/7) x 147 = 462 sq cm.
Q20. A sector has area 154 sq cm and radius 14 cm. Find its central angle.
- A) 45 degree
- B) 60 degree
- C) 90 degree
- D) 120 degree
Answer: C Explanation: (Theta/360) x (22/7) x 14 x 14 = 154 Theta = 90 degree.
Q21. Find the area of the largest circle that can fit inside a square of side 20 cm.
- A) 100pi sq cm
- B) 200pi sq cm
- C) 400pi sq cm
- D) 50pi sq cm
Answer: A Explanation: Diameter = side = 20 cm Radius = 10 cm Area = pi x 10^2 = 100pi sq cm.
Q22. A circular path has outer radius 14 cm and inner radius 7 cm. Find its area.
- A) 462 sq cm
- B) 308 sq cm
- C) 154 sq cm
- D) 616 sq cm
Answer: A Explanation: Area = pi(R^2 - r^2) = (22/7)(196 - 49) = 462 sq cm.
Q23. Find the circumference of a circle whose radius is 17.5 cm.
- A) 88 cm
- B) 99 cm
- C) 110 cm
- D) 121 cm
Answer: C Explanation: Circumference = 2 x (22/7) x 17.5 = 110 cm.
Q24. The area of a sector with angle 45 degree and radius 28 cm is:
- A) 308 sq cm
- B) 616 sq cm
- C) 154 sq cm
- D) 462 sq cm
Answer: A Explanation: Area = (45/360) x (22/7) x 28 x 28 = 308 sq cm.
Q25. Find the area of a circle whose diameter is 42 cm.
- A) 1386 sq cm
- B) 2772 sq cm
- C) 693 sq cm
- D) 462 sq cm
Answer: A Explanation: Radius = 21 cm Area = (22/7) x 21 x 21 = 1386 sq cm.
Q26. A clock minute hand is 21 cm long. Find the area swept in 10 minutes.
- A) 231 sq cm
- B) 154 sq cm
- C) 77 sq cm
- D) 462 sq cm
Answer: A Explanation: Angle swept in 10 min = 60 degree Area = (60/360) x (22/7) x 21 x 21 = 231 sq cm.
Q27. Find the length of an arc subtending 60 degree at the center of radius 21 cm.
- A) 11 cm
- B) 22 cm
- C) 44 cm
- D) 66 cm
Answer: B Explanation: Arc length = (60/360) x 2pi r = (1/6) x 2 x (22/7) x 21 = 22 cm.
Q28. The ratio of areas of two circles with radii 7 cm and 14 cm is:
- A) 1:2
- B) 1:4
- C) 2:1
- D) 4:1
Answer: B Explanation: Ratio of areas = r1^2 : r2^2 = 7^2 : 14^2 = 49 : 196 = 1 : 4.
Q29. A circle and a square have equal perimeters. If the circle radius is 14 cm, find the side of the square.
- A) 11 cm
- B) 22 cm
- C) 44 cm
- D) 88 cm
Answer: B Explanation: Circumference of circle = 2 x (22/7) x 14 = 88 cm Perimeter of square = 88 cm Side = 88/4 = 22 cm.
Q30. Find the area of a circle whose circumference is 132 cm.
- A) 1386 sq cm
- B) 693 sq cm
- C) 346.5 sq cm
- D) 462 sq cm
Answer: A Explanation: 2pi r = 132 2 x (22/7) x r = 132 r = 21 cm Area = (22/7) x 21 x 21 = 1386 sq cm.
Important Formulas
The following formulas are extremely important for solving Areas Related to Circles MCQs Class 10 and board exam questions.
| Formula Name | Formula |
| Area of Circle | πr² |
| Circumference of Circle | 2πr |
| Area of Sector | (θ/360) × πr² |
| Arc Length | (θ/360) × 2πr |
| Area of Semicircle | (1/2) × πr² |
| Perimeter of Semicircle | πr + 2r |
Important Terms Students Must Understand
The following terms are very important for solving Areas Related to Circles Class 10 MCQs with Answers.
| Term | Meaning |
| Radius | Distance from center to boundary |
| Diameter | Double of radius passing through center |
| Sector | Region enclosed by two radii and an arc |
| Segment | Region enclosed by chord and arc |
| Arc | Curved part of circle boundary |
| Circumference | Total boundary length of circle |
| Central Angle | Angle formed at center of circle |
