circle

level – 1

1. The area (in sq. cm) of the largest circle that can be drawn inside a square of side 14 cm is:(Take π = 22/7)
(a) 154
(b) 308
(c) 616
(d) 462

2. If the circumference of a circle increases from 6π cm to 10π cm, what is the increase in its area?
(a) 16π cm²
(b) 24π cm²
(c) 28π cm²
(d) 32π cm²

3. Three circles of radius 7 cm each are placed in such a way that each touches the other two. The area of the portion enclosed by the circles is:
(a) 49(2√3 − π) cm²
(b) 98(2√3 − π) cm²
(c) 49(√3 − π) cm²
(d) 196(2√3 − π) cm²

4. Four equal circles each of radius 7 cm touch one another. The area enclosed between them (Take π = 22/7), in square cm, is:
(a) 36
(b) 42
(c) 49
(d) 84

5. Three coins of radius 7 cm each are placed on a table such that each touches the other two. The area enclosed by the coins (Take π = 22/7) is:
(a) 49(√3 − 11/7) cm²
(b) 49(√3 − 22/7) cm²
(c) 49√3 − 77 cm²
(d) 49√3 − 154 cm²

6. The area of the largest triangle that can be inscribed in a semicircle of radius 7 cm is:
(a) 24.5 cm²
(b) 49 cm²
(c) 77 cm²
(d) 98 cm²

7. The area of a circle of radius 12 cm is trisected by two concentric circles. The radius of the smallest circle is:
(a) 4 cm
(b) 6 cm
(c) 8 cm
(d) 12 cm

8. Four equal circles of radius 7 cm are drawn at the four corners of a square and each touches the adjacent ones externally. The area of the portion between the square and the four sectors (Take π = 22/7) is:
(a) 84 cm²
(b) 98 cm²
(c) 112 cm²
(d) 196 cm²

9. The radius of circle P is three times that of circle Q, and the radius of circle Q is twice that of circle R. The ratio of their areas is:
(a) 36 : 4 : 1
(b) 9 : 4 : 1
(c) 18 : 6 : 1
(d) 12 : 4 : 1

10. A 14 m wide road runs outside around a circular park whose circumference is 88 m. The area of the road (Take π = 22/7) is:
(a) 1232 m²
(b) 1848 m²
(c) 2464 m²
(d) 3696 m²

11. The area of a circle is increased by 44 cm² when its radius is increased by 2 cm. The original radius of the circle is (Take π = 22/7):
(a) 3 cm
(b) 5 cm
(c) 7 cm
(d) 9 cm

12. The radii of two circles are 6 cm and 8 cm. The area of a third circle is equal to the sum of the areas of the two circles. The radius of the third circle is:
(a) 9 cm
(b) 10 cm
(c) 12 cm
(d) 14 cm

13. The ratio between the areas of two circles is 9 : 16. What is the ratio of their radii?
(a) 9 : 16
(b) 3 : 4
(c) 4 : 3
(d) 81 : 256

14. The diameters of two circles are equal to the side and the diagonal of a square of side 14 cm. The ratio of the area of the smaller circle to that of the larger circle is:
(a) 1 : 2
(b) 1 : √2
(c) 2 : 1
(d) 1 : 4

15. The radii of two circles are 9 cm and 40 cm. The radius of a circle whose area is equal to the sum of the areas of these two circles is:
(a) 41 cm
(b) 49 cm
(c) 50 cm
(d) 81 cm

16. The area of the greatest circle that can be inscribed in a square of side 28 cm is (Take π = 22/7):
(a) 616 cm²
(b) 1232 cm²
(c) 1540 cm²
(d) 2464 cm²

17. If the area of a circle inscribed in a square is 16π cm², then the area of the square is:
(a) 16 cm²
(b) 32 cm²
(c) 64 cm²
(d) 128 cm²

18. The area of a circle inscribed in a square of area 16 m² is:
(a) 4π m²
(b) 8π m²
(c) 16π m²
(d) 32π m²

19. The area of the square inscribed in a circle of radius 5 cm is:
(a) 25 cm²
(b) 50 cm²
(c) 75 cm²
(d) 100 cm²

20. A circle is inscribed in a square and a square is inscribed in that circle. The ratio of the area of the outer square to the inner square is:
(a) 1 : 1
(b) 2 : 1
(c) 1 : 2
(d) 4 : 1
21. Between a square of perimeter 56 cm and a circle of circumference 56 cm (Take π = 22/7), which figure has the larger area and by how much?
(a) square, by 28 cm²
(b) square, by 14 cm²
(c) circle, by 28 cm²
(d) circle, by 14 cm²

22. The perimeter of a square and a circular field are the same. If the area of the circular field is 2464 m² (Take π = 22/7), then the area of the square is:
(a) 1600 m²
(b) 1936 m²
(c) 2116 m²
(d) 2304 m²

23. A wire, when bent in the form of a square, encloses a region having area 196 cm². If the same wire is bent into the form of a circle (Take π = 22/7), then the area of the circle is:
(a) 308 cm²
(b) 616 cm²
(c) 154 cm²
(d) 462 cm²

24. A copper wire is bent in the form of an equilateral triangle and encloses an area of 49√3 cm². If the same wire is bent into the form of a circle (Take π = 22/7), the area (in cm²) enclosed by the wire is:
(a) 77
(b) 154
(c) 308
(d) 616

25. A circle and a square have equal areas. If π = 4, then the ratio of the side of the square to the radius of the circle is:
(a) 1 : 1
(b) 2 : 1
(c) 1 : 2
(d) 4 : 1

26. The diameter of a circle is equal to the side of a square. The ratio of the area of the circle to the area of the square (Take π = 22/7) is:
(a) 11 : 7
(b) 22 : 7
(c) 11 : 14
(d) 7 : 11

27. If the diameter of a circle is reduced by 20%, the area of the circle will be reduced by:
(a) 20%
(b) 36%
(c) 40%
(d) 64%

28. If the radius of a circle is increased by 20%, the area of the circle is increased by:
(a) 20%
(b) 40%
(c) 44%
(d) 60%

29. The radius of a circle is increased by 5%. By what percent does the area of the circle increase?
(a) 5%
(b) 10%
(c) 10.25%
(d) 25%

30. If the diameter of a circle is increased by 20%, then its area is increased by:
(a) 20%
(b) 36%
(c) 40%
(d) 44%

31. Two circles with centres P and Q and radius 3 units touch each other externally at R. A third circle with centre R and radius 3 units meets the other two at S and T. The area of the quadrilateral PQST is:
(a) 9√3
(b) 18√3
(c) 27√3
(d) 36√3

32. The difference between the radii of two circles is 7 cm. The difference between their areas is 462 cm² (Take π = 22/7). The radius of the smaller circle is:
(a) 7 cm
(b) 10 cm
(c) 14 cm
(d) 21 cm

33. If the diagonal of a square is equal to the diameter of a circle, then the ratio of the area of the square to that of the circle is (Take π = 22/7):
(a) 7 : 11
(b) 11 : 7
(c) 14 : 11
(d) 22 : 7

34. If the numerical value of the circumference and the area of a circle are the same, then the area of the circle is (Take π = 22/7):
(a) 154 cm²
(b) 44 cm²
(c) 88/7 cm²
(d) 308 cm²

35. A wire is bent into the form of a circle whose area is 616 cm². If the same wire is bent into the form of a square, then the area (in cm²) of the square is (Use π = 22/7):
(a) 784 cm²
(b) 770 cm²
(c) 756 cm²
(d) 800 cm²

35. A wire is bent into the form of a circle whose area is 616 cm². If the same wire is bent into the form of a square, then the area (in cm²) of the square is (Use π = 22/7):
(a) 784 cm²
(b) 770 cm²
(c) 756 cm²
(d) 800 cm²

36. The outer and inner diameters of a circular path are 840 m and 812 m respectively. The breadth of the path is:
(a) 12 m
(b) 14 m
(c) 16 m
(d) 18 m

37. The perimeter of a triangle is 24 cm and the circumference of its in-circle is 44 cm. The area of the triangle is:
(a) 72 cm²
(b) 84 cm²
(c) 96 cm²
(d) 108 cm²

38. The areas of a circle and a square are equal. If π = 22/7, then the ratio of the side of the square to the radius of the circle is:
(a) √(22/7)
(b) √(7/22)
(c) 22/7
(d) 7/22

39. A circle and a square have the same area. If the area of each is 196 cm², then the radius of the circle (take π = 1) is:
(a) 7 cm
(b) 14 cm
(c) 21 cm
(d) 28 cm

level – 2

1. The diameter of a bicycle wheel is 28 cm. What distance will it travel in 25 revolutions? (Take π = 22/7)
(a) 2000 cm
(b) 2100 cm
(c) 2200 cm
(d) 2400 cm

2. Diameter of a wheel is 7 cm. The wheel revolves 44 times in a minute. How much time will it take to cover a distance of 9.24 km? (Take π = 22/7)
(a) 1000 minutes
(b) 1500 minutes
(c) 2000 minutes
(d) 2500 minutes

3. The radius of a circular wheel is 3.5 m. How many revolutions will it make in travelling 22 km? (Take π = 22/7)
(a) 500
(b) 750
(c) 1000
(d) 1500

4. A circular wire of radius 49 cm is bent into a rectangle whose sides are in the ratio 4 : 3. The smaller side of the rectangle is:
(a) 44 cm
(b) 55 cm
(c) 66 cm
(d) 77 cm

5. The number of revolutions a wheel of diameter 35 cm makes in travelling a distance of 220 m is: (Take π = 22/7)
(a) 150
(b) 180
(c) 200
(d) 250

6. If the difference between the circumference and the diameter of a circle is 44 cm, then the radius of the circle is: (Take π = 22/7)
(a) 7 cm
(b) 11 cm
(c) 14 cm
(d) 21 cm

7. The radii of two circles are 7 cm and 14 cm. The ratio of their circumferences is:
(a) 1 : 2
(b) 2 : 1
(c) 7 : 14
(d) 14 : 7

8. The length (in cm) of a chord of a circle of radius 25 cm at a distance of 24 cm from its centre is:
(a) 10 cm
(b) 14 cm
(c) 18 cm
(d) 20 cm

9. A wheel makes 100 revolutions in moving 22 m. The diameter (in metres) of the wheel is:
(a) 0.5 m
(b) 0.7 m
(c) 0.77 m
(d) 0.8 m

10. A chord of length 24 cm is at a distance of 7 cm from the centre of a circle. What is the length of the chord of the same circle which is at a distance of 20 cm from the centre?
(a) 18 cm
(b) 30 cm
(c) 42 cm
(d) 48 cm

11. A circular path runs around a circular park. If the difference between the circumference of the outer circle and the inner circle is 88 metres, then the width of the path is (Use π = 22/7):
(a) 12 m
(b) 14 m
(c) 16 m
(d) 18 m

12. The ratio of the outer and the inner perimeter of a circular path is 9 : 8. If the path is 4 metres wide, then the diameter of the inner circle is:
(a) 56 m
(b) 60 m
(c) 64 m
(d) 72 m

13. If the area of a circle (Use π = 22/7) is equal to the area of a square whose side is 14√11 cm, then the ratio of the perimeter of the circle to the perimeter of the square is:
(a) 11 : 7
(b) 22 : 7
(c) 7 : 11
(d) 1 : 1

14. The length of a side of a square inscribed in a circle is √2 units. Find the circumference of the circle.
(a) 2π units
(b) 4π units
(c) 3π units
(d) π units

level – 3

1. Two circles have arcs of the same length. These arcs subtend angles of 45° and 60° at the centers of the circles. The ratio of their radii is:
(a) 4 : 3
(b) 3 : 4
(c) 5 : 4
(d) 4 : 5

2. A chord of length 24 cm is at a distance of 5 cm from the center of a circle. The radius of the circle is:
(a) 12 cm
(b) 13 cm
(c) 14 cm
(d) 15 cm

sector of circle

1. A sector of a circle has a radius of 6 cm. If the length of the arc is 6 cm, the area of the sector is:
(a) 18 cm²
(b) 12 cm²
(c) 15 cm²
(d) 10 cm²

2. A circle has a radius of 6 cm. A sector of the circle has a central angle of 60°. The area of the sector is:
(a) 18 cm²
(b) 12 cm²
(c) 6 cm²
(d) 24 cm²

semi circle

level – 1

1. The perimeter of a semicircular path is 36 m. Find the area of the semicircular path. (Take π = 22/7)
(a) 49 m²
(b) 63 m²
(c) 77 m²
(d) 98 m²

2. If a wire is bent into the shape of a square, the area of the square is 49 sq. cm. When the wire is bent into a semicircular shape (only curved part), find the area of the semicircle. (Take π = 22/7)
(a) 154 sq. cm
(b) 77 sq. cm
(c) 38.5 sq. cm
(d) 98 sq. cm

3. A copper wire is bent in the shape of a square of area 121 cm². If the same wire is bent in the form of a semicircle (only curved part), the radius (in cm) of the semicircle is:
(a) 7
(b) 14
(c) 11
(d) 22

level – 1

1. A semicircular shaped window has diameter 28 cm. Its perimeter equals:
(a) 72 cm
(b) 88 cm
(c) 66 cm
(d) 44 cm

2. A gear 15 cm in diameter is turning a gear 20 cm in diameter. When the smaller gear makes 40 revolutions, how many revolutions does the larger gear make?
(a) 20
(b) 25
(c) 30
(d) 35

3. The perimeter of a semicircle is 36 cm. The radius is:
(a) 5 cm
(b) 6 cm
(c) 7 cm
(d) 8 cm

4. A semicircular sheet of metal of diameter 42 cm is bent into an open conical cup. Find the capacity of the cup. (Take π = 22/7)
(a) 1232 cm³
(b) 2156 cm³
(c) 3080 cm³
(d) 4312 cm³

ANSWERS