# MCQs for Class 10 Maths Chapter 13 Surface Areas and Volumes

MCQs for Class 10 Maths Chapter 13 Surface Areas and Volumes: In this article, we have covered all the important MCQs for Free for Class 10 Term 1 2021-22 Board Exams. In accordance with the latest pattern, Padhle is here with MCQ Questions for Class 10.

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# Class 10 Maths Chapter 13 Surface Areas and Volumes MCQ

1.A cylindrical pencil sharpened at one edge is the combination of

(a) a cone and a cylinder

(b) frustum of a cone and a cylinder

(c) a hemisphere and a cylinder

(d) two cylinders.

Answer: (a) a cone and a cylinder

2. If the surface areas of two spheres are in ratio 16 : 9, then their volumes will be in the ratio:

(a) 27 : 64

(b) 64 : 27

(c) 4 : 3

(d) 3 : 4

Answer: (b) 64 : 27

3.The lateral surface area of a right circular cone of height 28 cm and base radius 21 cm(in sq. cm) is:

(a)2310

(b)2110

(c)1055

(d)1155

Answer: (a) 2310

4. A cylindrical pencil sharpened at one edge is the combination of

(a) two cylinders

(b) a hemisphere and a cylinder

(c) a cone and a cylinder

(d) frustum of a cone and a cylinder

Answer: (c) a cone and a cylinder

5. The base area of the cylinder is 80 sq.cm. If its height is 5cm, then its volume is

(a) 200 cu.cm

(b) 80 cu.cm

(c) 100 cu.cm

(d) 400 cu.cm

Answer: (d) 400 cu.cm

6. A cylinder and a cone are of the same base radius and same height. Find the ratio of the volumes of the cylinder of that of the cone.

(a) 1 : 3

(b) 1 : 2

(c) 3 : 1

(d) 2 : 1

Answer:(b) 1 : 2

7. A cone is cut through a plane parallel to its base and then the cone that is for medon one side of that plane is removed. The new part that is left over on the other side of the plane is called

(a) a frustum of a cone

(b) cone

(c) cylinder

(d) sphere

Answer: (a) a frustum of a cone

8. A cylinder, a cone and a hemisphere are of equal base and have the same height. What is the ratio of their volumes?

(a) 3 : 1 : 2

(b) 3 : 2 : 1

(c) 1 : 2 : 3

(d) 1 : 3 : 2

Answer: (a) 3 : 1 : 2

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9. If the ratio of the radius of a cone and a cylinder of equal volume is 3:5, then find the ratio of their heights.

(a)25/3

(b)28/3

(c)23/3

(d)7

Answer: (a) 25/3

10. A shuttlecock used for playing badminton has the shape of the combination of

(a) a cylinder and a sphere

(b) a sphere and a cone

(c) a cylinder and a hemisphere

(d) frustum of a cone and a hemisphere

Answer: (d) frustum of a cone and a hemisphere

11. A bucket of height 12 cm, has a top and bottom diameter of 40 cm and 20 cm respectively. The cost of tin sheet used for making the bucket at the rate of Rs. 1.20 per dm2 will be

(a) Rs. 21.44

(b) Rs 45.50

(c) Rs. 60.45

(d) Rs. 20.67

Answer: (a) Rs. 21.44

12. A toy is in the form of a cone mounted on a hemisphere of common base radius 7 cm. The total height of the toy is 31 cm. Find the total surface area of the toy.

(a) 465

(b) 912

(c) 769

(d) 858

Answer: (d) 858

13. During conversion of a solid from one shape to another, the volume of the new shape will

(a) increase

(b) decrease

(c) remain unaltered

(d) be doubled

Answer: (c) remain unaltered

14. If the area of three adjacent faces of cuboid are X, Y and Z respectively, then the volume of cuboid is:

(a) XYZ

(b) 3XYZ

(c) √xyz

(d) √3xyz

Answer: (c) √xyz

15. An iron rod of diameter 1cm and length 8cm is drawn into a wire of length 18m of uniform thickness. Find the thickness of the wire?

(a)0.09cm

(b)0.08cm

(c)0.06cm

(d) 0.05cm

Answer: (c)0.06cm

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16. The slant height of the frustum of a cone having radii of two ends as 5 cm and 2 cm respectively and height 4 cm is

(a) √26 cm

(b) 5 cm

(c) √65 cm

(d) 25 cm

Answer: (b) 5 cm

17. If the volume of a cube is 343 cm , then its edge is

(a) 9cm

(b) 8cm

(c) 49cm

(d) 7cm

Answer: (d) 7cm

18. What is the area of a semi–circle of radius 5 cm?

(a) 78.57 cm

(b) 71.42 cm

(c) 63.18 cm

(d) 79.86 cm

Answer: (a) 78.57 cm

19. A right circular cylinder of radius r cm and height h cm (h>2r) just encloses a sphere of diameter

(a) r cm

(b) 2r cm

(c) h cm

(d) 2h cm

Answer: (b) 2r cm

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20. The volumes of two spheres are in the ratio 27 : 8. The ratio of their curved surface is:

(a) 9 : 4

(b) 4 : 9

(c) 3 : 2

(d) 2 : 3

Answer: (a) 9 : 4

21. What do you understand by the quantity called ‘area’?

(a) It is the height of an object

(b) It is the quantity that expresses the extent of a planar 2-D surface

(c) It is the length of an object

(d)It is the quantity of an object

Answer: (b) It is the quantity that expresses the extent of a planar 2-D surface]

22. The total surface area of a hemispherical solid having radius 7 cm is

(a) 462 cm²

(b) 294 cm²

(c) 588 cm²

(d) 154 cm²

Answer: (a) 462 cm²

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23.The radii of the circular ends of a conical curd container, 6 cm high are 16 cm and 24 cm. The volume of the container in litres will be

(a) 6.75 litres

(b) 8.5 litres

(c) 6 litres

(d) 7.64 litres

Answer:(d) 7.64 litres

24. A hollow cube of internal edge 22cm is filled with spherical marbles of diameter 0.5 cm and it is assumed that 1/8th space of the cube remains unfilled. Then the number of marbles that the cube can accommodate is

(a) 142244

(b) 142396

(c) 142496

(d) 142596

Answer: (a) 142244

25. The ratio of the volumes of two spheres is 8 : 27. If r and R are the radii of spheres respectively, then (R – r): r is:

(a) 1 : 2

(b) 1 : 3

(c) 2 : 3

(d) 4 : 9

Answer: (a) 1 : 2

26. A solid metallic sphere of diameter 21 cm is melted and recast into a number of smaller cones, of diameter 3.5 cm and height 3cm. The number of cones so formed is:

(a)254

(b)504

(c)540

(d)405

Answer: (b)504

27. A solid formed on revolving a right angled triangle about its height is

(a) cylinder

(b) sphere

(c) right circular cone

(d) two cones

Answer: (c) right circular cone

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28. An open container made up of a metal sheet is in the form of a frustum of a cone of height 8 cm with radii of its lower and upper ends as 4 cm and 10 cm respectively. The cost of the oil at the rate of Rs. 50 per litre, which can completely fill the container, will be

(a) Rs. 45.60

(b) Rs. 76.50

(c) Rs.65.50

(d) Rs.70

Answer: (c) Rs.65.50

29. A metallic spherical shell of internal and external diameters 4 cm and 8 cm respectively, is melted and recast into the form of a cone with base diameter 8cm. The height of the cone is

(a) 12cm

(b) 14cm

(c) 15cm

(d) 18cm

Answer: (b) 14cm

30. The radii of two cylinders are in the ratio 2 : 3 and their heights are in the ratio 5 : 3. The ratio of their volumes is:

(a) 27 : 20

(b) 20 : 27

(c) 9 : 4

(d) 4 : 9

Answer: (b) 20 : 27

31. How many dimensions are required to make a cuboid?

(a) 3

(b) 1

(c) 15

(d) 100

Answer: (A)3

32. The surface area of a sphere is 616 cm2. Its radius is

(a) 7 cm

(b) 14 cm

(c) 21 cm

(d) 28 cm

Answer: (a) 7 cm

33.The ratio of the volume of a cube to that of a sphere which will exactly fit inside the cube is

(a) π : 8

(b) 6 : π

(c) π : 2

(d) 8 : π

Answer: (b) 6 : π

34. A solid piece of iron in the form of a cuboid of dimensions 49cm × 33cm × 24cm, is moulded to form a solid sphere. The radius of the sphere is

(a) 21cm

(b) 23cm

(c) 25cm

(d) 19cm

Answer: (a) 21cm

35. If the radius of base of a right circular cylinder is halved, keeping the height same, the ratio of the volume of the reduced cylinder to that of the original cylinder is:

(a) 2 : 3

(b) 3 : 4

(c) 1 : 4

(d) 4 : 1

Answer: (c) 1 : 4

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36. There are 2 identical cubes each having a total surface area equal to ‘A’. Let ‘S’ be the surface area of the solid obtained by joining these 2 cubes end to end. Which of the following statements is true?

(a)Cannot be determined

(b)S < 2A

(c)S > 2A

(d)S = 2A

Answer: (b) S < 2A

37. If a solid right circular cone of height 24 cm and base radius 6 cm is melted and recast in the shape of a sphere, then the radius of the sphere is

(a) 6 cm

(b) 12 cm

(c) 8 cm

(d) 4 cm

Answer:(a) 6 cm

38. If two solid hemispheres of same base radii r, are joined together along their bases, then curved surface area of this new solid is

(a) 4πr^{2}

(b) 6πr^{2}

(c) 3πr^{2}

(d) 8πr^{2}

Answer: (a) 4πr^{2}

39. If the volumes of a cube is 1728 cm³, the length of its edge is equal to:

(a) 7 cm

(b) 12 cm

(c) 18 cm

(d) 19 cm

Answer: (b) 12 cm

40. A piece of cloth is required to completely cover a solid object. The solid object is composed of a hemisphere and a cone surmounted on it. If the common radius is 7 m and height of the cone is 1 m, what is the area of cloth required?

(a)262.39m2

(b)463.39m2

(c)662.39m2

(d)563m2

Answer: (b) 463.39m2

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41. A cylinder and a cone are of same base radius and of same height. The ratio of the volume of the cylinder to that of the cone is

(a) 2 : 1

(b) 3 : 1

(c) 2 : 3

(d) 3 : 2

Answer: (b) 3 : 1

42. If two solid hemispheres of same base radius ‘x’ cm are joined together along their bases, then the CSA of the new solid formed is

(a) 8πx^{2} cm^{2}

(b) 6πx^{2} cm^{2}

(c) 5πx^{2} cm^{2}

(d) 4πx^{2} cm^{2}

Answer: (d) 4πx^{2} cm^{2}

43. A solid cylinder of radius r and height h is placed over other cylinder of same height and radius. The total surface area of the shape so formed is

(a) 4πrh + 4πr^{2}

(b) 4πrh − 4πr^{2}

(c) 4πrh + 2πr^{2}

(d) 4πrh − 2πr^{2}

Answer: (c) 4πrh + 2πr^{2}

44. The volume (in cm³) of the largest right circular cone that can be cut off from a cube of edge 4.2 cm is: .

(a) 9.7

(b) 72.6

(c) 58.2

(d) 19.4

Answer: (d) 19.

45. Ram has a semicircular disc. He rotates it about its diameter by 360 degrees. When he rotates the disc, a volume of air in his room gets swept. What is the name of the object/shape that exactly occupies this volume?

(a) Cylinder

(b) Hemisphere

(c) Sphere

(d) Cuboid

**Answer:** (c) Sphere

46. The volume of a sphere is 4851 cm3. Its diameter is

(a) 3.5 cm

(b) 7 cm

(c) 14 cm

(d) 21 cm

Answer: (d) 21 cm

47. The largest possible sphere is carved out from a cube of 7 cm side. The volume of the sphere will be

(a) 179.66 cm^{3}

(b) 185 cm^{3}

(c) 145 cm^{3}

(d) 125.55 cm^{3}

Answer: (a) 179.66 cm^{3}

48. A medicine-capsule is in the shape of a cylinder of diameter 0.5 cm with two hemispheres stuck to each of its ends. The length of entire capsule is 2 cm. The capacity of the capsule is

(a) 0.36 cm^{3}

(b) 0.35 cm^{3}

(c) 0.34 cm^{3}

(d) 0.33 cm^{3}

Answer: (a) 0.36 cm^{3}

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49. The circumference of the edge of hemispherical bowl is 132 cm. When π is taken as 22/7, the capacity of bowl in cm³ is:

(a) 2772

(b) 924

(c) 19404

(d) 9702

Answer: (a) 2772

50. A bucket is in the form of a frustum of a cone, its depth is 15 cm and the diameters of the top and the bottom are 56 cm and 42 cm respectively. How many liters of water can the bucket hold?

(a)28.49

(b)7.5

(c)2.5

(d)10

**Answer:** (a) 28.49

51. A piece of paper is in the shape of a semi¬circular region of radius 10 cm. It is rolled to form a right circular cone. The slant height is

(a) 5 cm

(b) 10 cm

(c) 15 cm

(d) 20 cm

Answer:(b) 10 cm

52. A cubical block of side 7 cm is surmounted by a hemisphere. The greatest diameter of the hemisphere is

(a) 3.5cm

(b) 14cm

(c) 10.5cm

(d) 7cm

Answer: (d) 7cm

53. Twelve solid spheres of the same size are made by melting a solid metallic cylinder of base diameter 2 cm and height 16 cm. The diameter of each sphere is

(a) 4 cm

(b) 3 cm

(c) 2 cm

(d) 6 cm

Answer: (c) 2 cm

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54. The surface areas of two spheres are in the ratio 1 : 2. The ratio of their volume is:

(a) √2 : 1

(b) 1 : 2√2

(c) 1 : 8

(d) 1 : 4

Answer: (b) 1 : 2√2

55. A 20 m deep well of diameter 7 m is dug and the earth taken out is evenly spread out to form a platform of 22 m by 14 m. Find the height of the platform (in m).

(a)7.5

(b)2.5

(c)10

(d)5

Answer: (b) 2.5

56. The base radii of two circular cones of the same height are in the ratio 3 : 5. The ratio of their volumes are

(a) 9 : 25

(b) 5 : 3

(c) 9 : 5

(d) 3 : 25

Answer: (a) 9 : 25

57. A container (open at the top) made up of metal sheet is in the form of a frustum of a cone of height 16 cm with radii of its lower and upper ends 8cm and 20 cm respectively. The amount of liquid the container can hold is (Take π = 3.14)

(a) 104.49 l

(b 10.95 l

(c) 12 l

(d) 10.45 l

Answer: (d) 10.45 l

58. The diameters of the two circular ends of the bucket are 44 cm and 24 cm. The height of the bucket is 35 cm. The capacity of the bucket is

(a) 32.7 litres

(b) 33.7 litres

(c) 34.7 litres

(d) 31.7 litres

Answer: (a) 32.7 litres

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59. The radius of spherical balloon increases from 8 cm to 12 cm. The ratio of the surface areas of balloon in two cases is:

(a) 2 : 3

(b) 3 : 2

(c) 8 : 27

(d) 4 : 9

Answer: (d) 4 : 9

60. A cylindrical tank is filled by pumping water from a cuboidal tank of dimensions 200cm × 150cm × 95 cm. The radius of the cylindrical tank is 60cm and height is 95cm. Find the height (in m) of the water left in the cuboidal tank after the cylindrical tank is completely filled. (Take π = 3.14)

(a)0.76 m

(b)0.69 m

(c)0.59 m

(d)0.45 m

Answer: (C) 0.59 m

61.The curved surface area of glass having radii 3 cm and 4 cm respectively and slant height 10 cm is

(a) 55 cm²

(b) 110 cm²

(c) 220 cm²

(d) 440 cm²

Answer: (c) 220 cm²

62. A cylinder, a cone and a hemisphere have equal base and height. Find the ratio of their volumes

(a) 1:1:1

(b 2:3:1

(c) 3 :1 :2

(d) 1:2:3

Answer: (c) 3 :1 :2

63. Volumes of two spheres are in the ratio 64:27. The ratio of their surface areas is:

(a) 3 : 4

(b) 4 : 3

(c) 9 : 16

(d) 16 : 9

Answer: (d) 16 : 9

64. Two cubes each of volume 8 cm³ are joined end to end, then the surface area of the resulting cuboid is:

(a) 80 cm²

(b) 64 cm²

(c) 40 cm²

(d) 8 cm²

Answer: (c) 40 cm²

65. A cylinder is moulded into the shape of a sphere. Which of the following factors will be same for both the shapes?

(a)None of these

(b)Curved surface area

(c)Surface area

(d)Volume

Answer: (D) Volume

66. If two solid hemispheres of same base radius are joined together along their bases, then curved surface area of this new solid is

(a) 3πr²

(b) 4πr²

(c) 5πr²

(d) 6πr²

Answer: (b) 4πr²

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67. A cone and a cylinder have their heights in the ratio 4: 5 and their diameters are in the ratio 3: 2. The ratio of their volumes will be

(a) 6: 7

(b) 4: 3

(c) 3: 5

(d) 5: 3

Answer: (c) 3: 5

68. A mason constructs a wall of dimensions 270cm× 300cm × 350cm with the bricks each of size 22.5cm × 11.25cm × 8.75cm and it is assumed that 1/8 space is covered by the mortar. Then the number of bricks used to construct the wall is:

(a) 11100

(b) 11200

(c) 11000

(d) 11300

Answer: (b) 11200

69. Taking π = 227, if surface area of a sphere is 616 cm², then its diameter is:

(a) 7 cm

(b) 14 cm

(c) 56 cm

(d) 28 cm

Answer: (b) 14 cm

70. The diameter of a sphere is 6 cm. It is melted and drawn into a wire of diameter 2 mm. The length of the wire is:

(a)66m

(b)36m

(c)18m

(d)12m

Answer: (b) 36m

71. The radii of the top and bottom of a bucket of slant height 13 cm are 9 cm and 4 cm respectively. The height of the bucket is

(a) 10 cm

(b) 12 cm

(c) 15 cm

(d) 16 cm

Answer: (b) 12 cm

72. The number of lead balls each of radius1 cm, that can be formed from a sphere of radius 8 cm will be

(a) 380

(b) 400

(c) 512

(d) 225

Answer: (c) 512

73. The area of the square that can be inscribed in a circle of radius 8 cm is (in cm²):

(a) 256

(b) 128

(c) 64√2

(d) 64

Answer: (b) 128

74. How many gold coins of 1.75cm in diameter and 2mm in thickness can be melted to form a cuboid of dimensions 5.5cm x 10cm x 3.5cm?

(a)400

(b)500

(c)350

(d)550

Answer: (A) 400

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75. The volume of the cuboid whose length, breadth and height is 12cm, 8cm and 6cm is

(a) 568 cu.cm

(b) 576 cu.cm

(c) 576 sq.cm

(d) 570 cu.cm

Answer: (b) 576 cu.cm

76. The curved surface area of a right circular cone of height 15 cm and base diameter 16 cm² is:

(a) 60π cm²

(b) 68π cm²

(c) 1200π cm²

(d) 136π cm²

Answer: (d) 136π cm²

77. What is a cylindrical pencil sharpened at one edge the combination of?

(a) a cone and a cylinder

(b) a hemisphere and a cylinder

(c) two cylinders

(d) frustum of a cone and a cylinder

Answer:(a) a cone and a cylinder

78. The inner dimensions of a closed box are 12cm, 10cm and 8cm. If the thickness of the wood is 1cm, then the capacity f the box is

(a) 1920 cu.cm

(b) 480 cu.cm

(c) 960 cu.cm

(d) 1200 cu.cm

Answer: (c) 960 cu.cm

79. The material of a cone is converted into the shape of a cylinder of equal radius. If the height of the cylinder is 5 cm, then the height of the cone is

(a) 15 cm

(b) 10 cm

(c) 18 cm

(d) 24 cm

Answer: (a) 15 cm

80. A shuttle cock used for playing badminton has the shape of a combination of:

(а) a cylinder and a sphere

(b) a cylinder and a hemisphere

(c) a cone and a sphere

(d) a frustum of a cone and a hemisphere

Answer: (d) a frustum of a cone and a hemisphere

81. Given that a right circular cylinder is of radius r cm and height h cm (h>2r), ** _** encloses a sphere of diameter

(a) 2r cm

(b) r cm

(c) 2h cm

(d) h cm

Answer: (b) r cm

82. A plumbline is combination of

(a) a hemisphere and a cylinder

(b) a sphere and a cylinder

(c) a hemisphere and a cone

(d) a cone and a cylinder

Answer: (c) a hemisphere and a cone

83. The radius of a wire is decreased to one third. If volume remains the same, the length will become:

(a) 3 times

(b) 6 times

(c) 9 times

(d) 27 times

Answer: (c) 9 times

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84. When twelve solid spheres of the same size are made by melting a solid metallic cylinder of base diameter 2 cm and height 16 cm. Then, calculate the diameter of each sphere.

(a) 4 cm

(b) 6 cm

(c) 3 cm

(d) 2 cm

Answer: (d) 2 cm

85. The diameter of a sphere is 6 cm. It is melted and drawn into a wire of diameter 2 cm. The length of the wire is

(a) 36 cm

(b) 18 cm

(c) 66 cm

(d) 12 cm

Answer: (a) 36 cm

86. The volume of a right circular cylinder is 345 cm³. Then, the volume of a right circular cone whose radius of the base and height is the same as of circular cylinder will be:

(a) 345 cm³

(b) 690 cm³

(c) 115 cm³

(d) 230 cm³

Answer: (c) 115 cm³

87. A largest sphere is carved out of a cube of side 7cm. The volume of the sphere is

(a) 176.42 cu.cm

(b) 180.5 cu.cm

(c) 179.67 cu.cm

(d) 182 cu.cm

Answer: (c) 179.67 cu.cm

88. The slant height of a bucket is 26 cm. The diameter of upper and lower circular ends are 36 cm and 16 cm. then height of bucket is:

(a) 22 cm

(b) 24 cm

(c) 10 cm

(d) 25 cm

Answer: (b) 24 cm

89. The edge of the cube whose volume is 1728cm is

(a) 17cm

(b) 12cm

(c) 18cm

(d) 72cm

Answer: (b) 12cm

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90.The volume (in cm³) of the largest right circular cone that can be cut off from a cube of edge 4.2 cm is:

(a) 9.7

(b) 77.6

(c) 58.2

(d) 19.4

Answer: (d) 19.4

91. If the surface area of the sphere is same as the CSA of a right circular cylinder whose height and diameter are 12cm each, then the radius of the sphere is

(a) 12cm

(b) 8cm

(c) 6cm

(d) 3cm

Answer: (c) 6cm

92. By melting a solid sphere of radius 5 cm a solid right circular cone of the same circular base radius is made. The height of cone is:

(a) 20 cm

(b) 10 cm

(c) 5 cm

(d) 12 cm

Answer: (a) 20 cm

93. A cylinder and a cone area of same base radius and of same height. The ratio of the volume of cylinder to that of cone is:

(a) 3 : 1

(b) 1 : 3

(c) 2 : 3

(d) 1 : 1

Answer: (a) 3 : 1

94. Eight solid sphere of same size are made by melting a solid metallic cylinder of base diameter 6 cm and height 32 cm. The diameter of each sphere is:

(a) 3 cm

(b) 6 cm

(c) 12 cm

(d) 8 cm

Answer: (b) 6 cm

95. The number of conical bottles of radius 2 cm and height 3.6 cm, required to empty the liquid from a cylindrical bottle of radius 6 cm and height 10 cm is:

(a) 100

(b) 9

(c) 75

(d) 20

Answer: (c) 75

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