12

Q1. Area of a sector of a circle of radius 36 cm is 54Π cm². The length of the corresponding arc of the sector is

2Π cm

3Π cm

4Π cm

5Π cm

Q2. The area of a circular plot is 9856 sq. m. The cost of fencing the plot at the rate of Rs. 7 per meter will be

Rs. 2000

Rs. 3456

Rs. 2464

Rs. 2211

Q3. The ratio between the radii of two circles is 1 : 5. Calculate the ratio between their circumferences.

1 : 2

1 : 5

1 : 6

1 : 8

Q4. The radius of a circle if its perimeter and area are numerically equal is

2 units

5 units

4 units

8 units

Q5. To warn ships of underwater rocks, a light house spreads a red colored light over a sector of angle 80^o to a distance of 16.5 km. The area of the sea over which the ships are warned is

190.14 km²

200 km²

180.5 km²

135.7 km²

Q6. The area and circumference of a circle are numerically equal. What is the diameter of the circle?

2 units

20 units

4 units

40 units

Q7. If the sum of the areas of two circles with radii R₁ and R₂ is equal to the area of a circle of radius R, then

R₁ + R₂ = R

R₁² + R₂² = R²

R₁ + R₂ < R

R₁² + R₂² < R²

Q8. If the radius of a circle is r and the side of a square is x, and the circle is inscribed in the square, then find the remaining area left in the square.

𝜋r²- x²

𝜋x²- r²

x²-𝜋r²

𝜋r²-2x²

Q9. The radii of two circles are 19 cm and 9 cm respectively. The radius of the circle which has its circumference equal to the sum of the circumferences of the two circles is:

28 cm

30 cm

26 cm

32 cm

Q10. The sum of the diameters of two circles is 280 cm and the difference of their circumferences is 88 cm. Then the larger of the two radii is

77 cm

63 cm

44 cm

cannot be determined

Q11. If the circumference of a circle increases from 2π to 4π then its area is

Halved

Doubled

Tripled

Four times

Q12. What is the area of the square inscribed in a circle with a circumference of 18.84 cm?

15 cm²

18 cm²

16 cm²

20 cm²

Q13. A pendulum swings through an angle of 30⁰ and describes an arc 8.8 cm in length. The length of the pendulum is

8.8 cm

15.8 cm

16.8 cm

17 cm

Q14. A circular disc of radius 6 cm is divided into three sectors with central angles 90^o, 120^o and 150^o. The ratio of the areas of the three sectors is

4: 5: 6

3: 4: 5

2: 3: 4

1: 5: 6

Q15. The minute hand of a clock is 10 cm long. The area of the face of the clock described by the minute hand between 8 A.M and 8.25 A.M is

120 cm²

130.95 cm²

100 cm²

125.5 cm²

Q16. A wire is bent in the form of a circle of radius 28 cm. It is rebent to form a square. The length of the side of the square will be

88 cm

30 cm

40 cm

44 cm

Q17. The area of the quadrant of a circle whose circumference is 22 cm, will be

9.625 cm²

15 cm²

10 cm²

96.25 cm³

Q18. The area of a circle with diameter 6 m exceeds the combined areas of circles with diameters 4 m and 2 m by

0 m²

2∏

4∏

∏

Q19. The angle of the major sector and the corresponding minor sector of a circle are

complementary angles

supplementary angles

Reflex angles

conjugate angles

Q20. The perimeter (in cm) of a square circumscribing a circle of radius a cm, is

8 a

4 a

2 a

16 a

Q21. The length of the line that marks out a circle and its region is the

Diameter

Radius

Chord

Circumference

Q22. The perimeter of a certain sector of a circle of radius 6.5 cm is 31 cm. The area of the sector will be

45 cm²

40 cm²

49 cm²

58.5 cm²

Q23. The diameter of a circle whose area is equal to the sum of the areas of the two circles of radii 24 cm and 7 cm is

31 cm

25 cm

62 cm

50 cm

Q24. The area of a sector of a circle of radius 5 cm is 5Π cm². The angle contained by the sector will be 

60^o

45^o

90^o

72^o

Q25. The length of a minute hand of a wall clock is 7 cm. What is the area swept by it is 30 minutes?

-3.208

3.208

2.308

3.608

Q26. From a circular sheet of paper with a radius 20 cm, four circles of radius 5 cm each are cut out. What is the ratio of the uncut to the cut portion?

1 : 3

4 : 1

3 : 1

4 : 3

Q27. If the diameter of semicircular protractor is 14 cm, then its perimeter will be

30 cm

36 cm

40 cm

44 cm

Q28. The diameter of a wheel is 42 cm. How many revolutions will it take to travel 462 m? 

353

352

351

350

Q29. The diameter of a wheel is 35 cm. How many revolutions will it make to travel 539 m? 

500

490

480

470

Q30. A wire in the shape of square of perimeter 88 cm is bent so as to form a circular ring. Find the radius of the ring.

22 cm

14 cm

28 cm

7 cm

Q31. Find the area of a semicircle of diameter 14 cm. 

154 cm²

616 cm²

77 cm²

38.5 cm²

Q32. Find the semi-perimeter of a circle of radius 21 cm. 

132 cm

108 cm

66 cm

27 cm

Q33. The diameter of a circle whose area is equal to the sum of the areas of the two circles of radii 40 cm and 9 cm is

41 cm

49 cm

82 cm

62 cm

Q34. A garden roller has a circumference of 4 m. The number of revolutions it makes in moving 40 metres are:

₁₂

16

8

10

Q35. The area swept by the minute hand of a circular clock in 5 minutes forms a

Sector

Cone

Segment

Circle

Q36. If the ratio of the arc AB to the circumference of a circle is1:3,then measure of the angle subtended by the arc at the centre is

72^o

120^o

172^o

65^o

Q37. The area of a circular pizza is 616 cm². Its diameter is

14 cm

20 cm

35 cm

28 cm

Q38. If the perimeter of a sector of a circle of radius 5.2 cm. is 16.4 cm. What multiple of the radius is the area of the sector?

2r

3r

4r

5r

Q39. The inner circumference of a circular track is 440 m, and the track is 14 m wide. The cost of levelling the track at 25 paise/m² will be

Rs. 1400

Rs. 1250

Rs. 1694

Rs. 1684

Q40. Three horses are tethered with 7 meter long ropes at the three corners of a triangular field having sides 20 m, 34 m and 42 m. The area of the plot which can be grazed by the horses is

80 m²

77 m²

100 m²

30 m²