MATHEMATICS CLASS- 10
MCQ- CH-11(Area related to circles)
Class 10 Mathematics
Chapter 11: Areas Related to Circles
50 Board-Level MCQs with Answers and Solutions
Q1. The circumference of a circle of radius 7 cm is
(a) 22 cm
(b) 44 cm
(c) 49 cm
(d) 154 cm
Answer: (b) 44 cm
Solution: Circumference = 2πr = 2 × 22/7 × 7 = 44 cm.
Q2. The area of a circle of radius 7 cm is
(a) 154 cm²
(b) 144 cm²
(c) 49 cm²
(d) 308 cm²
Answer: (a) 154 cm²
Solution: Area = πr² = 22/7 × 7 × 7 = 154 cm².
Q3. The area of a semicircle is
(a) πr²
(b) 2πr²
(c) ½πr²
(d) ¼πr²
Answer: (c) ½πr²
Q4. The area of a quadrant of radius r is
(a) πr²
(b) ½πr²
(c) ¼πr²
(d) ⅛πr²
Answer: (c)
Q5. The length of an arc of 90° in a circle of radius 14 cm is
(a) 22 cm
(b) 44 cm
(c) 11 cm
(d) 88 cm
Answer: (a) 22 cm
Solution: Arc Length = (90/360) × 2πr = 22 cm.
Q6. The area of a sector of angle 90° and radius 14 cm is
(a) 154 cm²
(b) 77 cm²
(c) 308 cm²
(d) 44 cm²
Answer: (a)
Q7. The formula for area of a sector is
(a) (θ/360) × πr²
(b) 2πr
(c) πr²
(d) θπr
Answer: (a)
Q8. The formula for length of an arc is
(a) (θ/360) × πr²
(b) (θ/360) × 2πr
(c) πr²
(d) 2πr²
Answer: (b)
Q9. Area of a circle of diameter 14 cm is
(a) 154 cm²
(b) 308 cm²
(c) 44 cm²
(d) 77 cm²
Answer: (a)
Q10. The circumference of a circle of diameter 21 cm is
(a) 44 cm
(b) 66 cm
(c) 77 cm
(d) 88 cm
Answer: (b)
Q11. A sector becomes a semicircle when central angle is
(a) 45°
(b) 90°
(c) 180°
(d) 360°
Answer: (c)
Q12. Area of a quadrant of radius 14 cm is
(a) 77 cm²
(b) 154 cm²
(c) 308 cm²
(d) 44 cm²
Answer: (b)
Q13. The area of a circle is directly proportional to
(a) r
(b) r²
(c) r³
(d) diameter
Answer: (b)
Q14. If radius doubles, area becomes
(a) Double
(b) Triple
(c) Four times
(d) Eight times
Answer: (c)
Q15. If radius doubles, circumference becomes
(a) Double
(b) Triple
(c) Four times
(d) Half
Answer: (a)
Q16. Area of a semicircle of radius 14 cm is
(a) 154 cm²
(b) 308 cm²
(c) 77 cm²
(d) 44 cm²
Answer: (b)
Q17. The perimeter of a semicircle includes
(a) Arc only
(b) Diameter only
(c) Arc + Diameter
(d) Radius only
Answer: (c)
Q18. Perimeter of a semicircle of radius 7 cm is
(a) 22 cm
(b) 36 cm
(c) 44 cm
(d) 28 cm
Answer: (b)
Solution: πr + 2r = 22 + 14 = 36 cm.
Q19. Area of a circle of radius 21 cm is
(a) 1386 cm²
(b) 1320 cm²
(c) 1400 cm²
(d) 1256 cm²
Answer: (a)
Q20. The area of a sector of angle 180° is
(a) Whole circle
(b) Semicircle
(c) Quadrant
(d) Arc
Answer: (b)
Q21. (CBSE PYQ) Length of arc of 60° in a circle of radius 21 cm is
(a) 22 cm
(b) 44 cm
(c) 66 cm
(d) 77 cm
Answer: (a)
Q22. Area of sector with angle 60° and radius 21 cm is
(a) 231 cm²
(b) 462 cm²
(c) 154 cm²
(d) 308 cm²
Answer: (a)
Q23. The area enclosed between two radii and an arc is called
(a) Segment
(b) Sector
(c) Chord
(d) Diameter
Answer: (b)
Q24. The region enclosed by a chord and its corresponding arc is called
(a) Sector
(b) Radius
(c) Segment
(d) Diameter
Answer: (c)
Q25. Area of a circle of radius 14 cm is
(a) 616 cm²
(b) 308 cm²
(c) 154 cm²
(d) 44 cm²
Answer: (a)
Q26. (CBSE PYQ) The circumference of a circle of radius 14 cm is
(a) 44 cm
(b) 66 cm
(c) 88 cm
(d) 154 cm
Answer: (c)
Q27. Area of a quadrant of radius 28 cm is
(a) 616 cm²
(b) 308 cm²
(c) 154 cm²
(d) 77 cm²
Answer: (a)
Q28. Arc length of a semicircle of radius 7 cm is
(a) 11 cm
(b) 22 cm
(c) 44 cm
(d) 14 cm
Answer: (b)
Q29. A full circle subtends an angle of
(a) 90°
(b) 180°
(c) 270°
(d) 360°
Answer: (d)
Q30. A quadrant subtends an angle of
(a) 45°
(b) 90°
(c) 180°
(d) 360°
Answer: (b)
Q31. Area of a sector of 120° in a circle of radius 14 cm is
(a) 205.3 cm²
(b) 154 cm²
(c) 102.6 cm²
(d) 308 cm²
Answer: (a)
Q32. If diameter is doubled, area becomes
(a) Double
(b) Triple
(c) Four times
(d) Eight times
Answer: (c)
Q33. If radius is halved, area becomes
(a) Half
(b) One-fourth
(c) One-third
(d) One-eighth
Answer: (b)
Q34. Perimeter of a quadrant of radius 14 cm is
(a) 50 cm
(b) 22 cm
(c) 44 cm
(d) 28 cm
Answer: (a)
Solution: Arc = 22 cm, two radii = 28 cm, total = 50 cm.
Q35. Which formula gives area of a circle?
(a) 2πr
(b) πr²
(c) πd
(d) r²
Answer: (b)
Q36. (CBSE PYQ) Area of a circle of radius 28 cm is
(a) 2464 cm²
(b) 1232 cm²
(c) 616 cm²
(d) 308 cm²
Answer: (a)
Q37. Length of arc of 180° is
(a) Quarter circumference
(b) Half circumference
(c) Full circumference
(d) Double circumference
Answer: (b)
Q38. Area of a sector depends on
(a) Radius only
(b) Central angle only
(c) Radius and central angle
(d) Diameter only
Answer: (c)
Q39. The circumference of a circle is also called its
(a) Area
(b) Boundary Length
(c) Radius
(d) Diameter
Answer: (b)
Q40. Area of a semicircle of radius 21 cm is
(a) 693 cm²
(b) 1386 cm²
(c) 346.5 cm²
(d) 462 cm²
Answer: (a)
Q41. If circumference is 44 cm, radius is
(a) 5 cm
(b) 6 cm
(c) 7 cm
(d) 8 cm
Answer: (c)
Q42. (CBSE PYQ) Area of a quadrant of radius 21 cm is
(a) 346.5 cm²
(b) 693 cm²
(c) 1386 cm²
(d) 231 cm²
Answer: (a)
Q43. If radius is 0, area of circle is
(a) 0
(b) 1
(c) π
(d) Undefined
Answer: (a)
Q44. Arc length is proportional to
(a) Radius only
(b) Central angle only
(c) Both radius and central angle
(d) Diameter only
Answer: (c)
Q45. The area of a circle is measured in
(a) cm
(b) cm²
(c) cm³
(d) degrees
Answer: (b)
Q46. The circumference of a circle is measured in
(a) cm²
(b) cm³
(c) cm
(d) degrees
Answer: (c)
Q47. If radius is 35 cm, circumference is
(a) 110 cm
(b) 220 cm
(c) 330 cm
(d) 440 cm
Answer: (b)
Q48. Area of a circle having diameter 28 cm is
(a) 308 cm²
(b) 616 cm²
(c) 154 cm²
(d) 1232 cm²
Answer: (b)
Q49. A sector with angle 360° represents
(a) Semicircle
(b) Quadrant
(c) Whole Circle
(d) Segment
Answer: (c)
Q50. Which statement is true?
(a) Area of a circle is proportional to radius.
(b) Circumference is proportional to radius.
(c) Area of a circle is proportional to square of radius.
(d) Both (b) and (c)
Answer: (d) Both (b) and (c)
Solution: Circumference = 2πr and Area = πr².