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

1. 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**

Answer: c

2. 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**

Answer: d

3. 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/ Explanation**

Answer: b

Explaination:

4. 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/ Explanation**

Answer: a

Explaination: Reason: Total surface area of hemisphere = 3πr² = 3 × \(\frac{22}{7}\) × 7 × 7 = 462 cm²

5. 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/ Explanation**

Answer: c

Explaination: Reason: Right circular cone is formed.

6. 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/ Explanation**

Answer: a

Explaination:

7. 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/ Explanation**

Answer: b

Explaination:

8. The volume of a sphere is 4851 cm^{3}. Its diameter is

(a) 3.5 cm

(b) 7 cm

(c) 14 cm

(d) 21 cm

**Answer/ Explanation**

Answer: d

Explaination:

9. 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/ Explanation**

Answer: b

Explaination: Reason: Slant height l = r

10. 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/ Explanation**

Answer: a

Explaination:

11. 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/ Explanation**

Answer: c

Explaination: Reason: Here r = 3 cm, R = 4 cm, l = 10 cm

∴ Curved surface area = πl(r + R) = \(\frac{22}{7}\) × 10(3 + 4)=\(\frac{22}{7}\) × 10 × 7 = 220 cm²

12. 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**

Answer: b

13. 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/ Explanation**

Answer: b

Explaination: l² = h² + (R-r)² => 13² = h² + (9 – 4)²

⇒ 169 = h² + 25

⇒ h² = 169 – 25

⇒ h² = 144

⇒ h = 12

14. A surahi is the combination of [NCERT Exemplar Problems]

(a) a sphere and a cylinder

(b) a hemisphere and a cylinder

(c) two hemispheres

(d) a cylinder and a cone

**Answer/ Explanation**

Answer: a

Explaination: (a) A sphere and a cylinder.

15. Match the column :

(a) 1 → A, 2 → C, 3 → D, 4 → E

(b) 1 → F, 2 → B, 3 → C, 4 → E

(c) 1 → B, 2 → C, 3 → D, 4 → E

(d) 1 → F, 2 → E, 3 → C, 4 → A

**Answer/ Explanation**

Answer: b

Explaination: (b) Formulae.

16. A cube whose edge is 20 cm long, has circles on each of its faces painted black. What is the total area of the unpainted surface of the cube if the circles are of the largest possible areas?

(a) 90.72 cm²

(b) 256.72 cm²

(c) 330.3 cm²

(d) 514.28 cm²

**Answer/ Explanation**

Answer: d

Explaination:

(d) Diameter of largest circle = 20 cm.

∴ Area of circle = 100π cm²

∴ Area of 6 circles = 6 × 100π = 600π cm² (∵ there are six faces in a cube)

Also, Area of cube = 6 × (20)² = 2400 cm²

Area of unpainted surface = 2400 – 600π

= 2400 – 600 × \(\frac{22}{7}\)

= 514.28 cm².

17. If two solid hemispheres of the same base radius r are joined together along their bases, then curved surface area of this new solid is [NCERT Exemplar Problems]

(a) 4πr²

(b) 6πr²

(c) 3πr²

(d) 8πr²

**Answer/ Explanation**

Answer: a

Explaination: (a) 4πr²

18. The radius (in cm) of the largest right circular cone that can be cut out from a cube of edge 4.2 cm is [AI2011]

(a) 4.2

(b) 2.1

(c) 8.1

(d) 1.05

**Answer/ Explanation**

Answer: b

Explaination:

(b) Edge of the cube = 4.2 cm

Diameter of base of largest possible cone = 4.2 cm 4 2

∴ Radius = \(\frac{4.2}{2}\) = 2.1 cm

19. How many bags of grain can be stored in a cuboid granary 12 m × 6 m × 5 m. If each bag occupies a space of 0.48 m^{3}?

(a) 750

(b) 75

(c) 1500

(d) 375

**Answer/ Explanation**

Answer: a

Explaination:

20. In a swimming pool measuring 90 m × 40 m, 150 men take a dip. If the average displacement of water by a man is 8 m3, then rise in water level is

(a) 27.33 cm

(b) 30 cm

(c) 31.33 cm

(d) 33.33 cm

**Answer/ Explanation**

Answer: d

Explaination:

(d) Volume of water displaced

= 150 × 8 = 1200 m^{3}

⇒ 90 × 40 × h = 1200

⇒ h = \(\frac{1200}{90 \times 40}\) m = 33.33 cm

21. Match the column:

(a) 1 → C, 2 → A, 3 → D, 4 → F

(b) 1 → C, 2 → A, 3 → D, 4 → E

(c) 1 → C, 2 → B, 3 → D, 4 → F

(d) 1 → C, 2 → A, 3 → F, 4 → D

**Answer/ Explanation**

Answer: c

Explaination: (c) Formulae.

22. Given that 1 cu. cm of marble weighs 25 g, the weight of a marble block of 28 cm in width and 5 cm thick, is 112 kg. The length of the block is

(a) 36 cm

(b) 37.5 cm

(c) 32 cm

(d) 26.5 cm

**Answer/ Explanation**

Answer: c

Explaination:

23. A sphere and a cube have equal surface areas. The ratio of the volume of the sphere to that of cube is

**Answer/ Explanation**

Answer: b

Explaination:

24. A sphere of diameter 18 cm is dropped into a cylindrical vessel of diameter 36 cm, partly filled with water. If the sphere is completely submerged, then the water level rises (in cm) by [Delhi 2011]

(a) 3

(b) 4

(c) 5

(d) 6

**Answer/ Explanation**

Answer: a

Explaination:

25. The shape of a gilli, in the gilli-danda game (see Fig.), is a combination of [NCERT Exemplar Problems]

(a) two cylinders

(b) a cone and a cylinder

(c) two cones and a cylinder

(d) two cylinders and a cone

**Answer/ Explanation**

Answer: c

Explaination: (c) Two cones and a cylinder.

26. A right circular cylinder of radius r cm and height h cm (h > 2r) just encloses a sphere of diameter [NCERT Exemplar Problems]

(a) r cm

(b) 2r cm

(c) h cm

(d) 2h cm

**Answer/ Explanation**

Answer: b

Explaination: (b) 2r cm.

27. During conversion of a solid from one shape to another, the volume of the new shape will [NCERT Exemplar Problems]

(a) increase

(B) decrease

(c) remain unaltered

(d) be doubled

**Answer/ Explanation**

Answer: c

Explaination: (c) Remain unaltered.

28. A rectangular block 6 cm × 12 cm × 15 cm is cut into exact number of equal cubes. The least possible number of cubes will be

(a) 6

(b) 11

(c) 33

(d) 40

**Answer/ Explanation**

Answer: d

Explaination:

(d) Volume of rectangular block = 6 × 12 × 15 = 1080 cm^{3}

Side of largest cube = HCF of 6, 12, 15

= 3

∴ Volume of 1 cube = 33 = 27 cm^{3}

Number of cubes = \(\frac{6 \times 12 \times 15}{27}\) = 40

29. Ariver 1.5 m deep and 36 m wide is flowing at the rate of 3.5 km per hour. The amount of water that runs into the sea per minute (in cubic metres) is

(a) 31500

(b) 3150

(c) 3150000

(d) 6300

**Answer/ Explanation**

Answer:

Explaination:

30. The number of coins, 1.5 cm in diameter and 0.2 cm thick to be melted to form a right circular cylinder of height 10 cm and diameter 4.5 cm is

(a) 350

(b) 400

(c) 450

(d) 500

**Answer/ Explanation**

Answer: c

Explaination:

31. The shape of a glass (tumbler) (see Fig.) is usually in the form of [NCERT Exemplar Problems]

(a) A cone

(b) frustum of a cone

(c) a cylinder

(d) a sphere

**Answer/ Explanation**

Answer: b

Explaination: (b) Frustum of a cone.

32. A shuttle cock used for playing badminton has the shape of the combination of [NCERT Exemplar Problems]

(a) a cylinder and a sphere

(b) a cylinder and a hemisphere

(c) a sphere and a cone

(d) frustum of a cone and a hemisphere

**Answer/ Explanation**

Answer: d

Explaination: (d) Frustum of a cone and a hemisphere.

33. A cone is cut through a plane parallel to its base and then the cone that is formed on one side of that plane is removed. The new part that is left over on the other side of the plane is called [NCERT Exemplar Problems]

(a) a frustum of a cone

(b) cone

(c) cylinder

(d) sphere

**Answer/ Explanation**

Answer: a

Explaination: (a) Frustum of a cone.

34. In a right circular cone, the cross-section made by a plane parallel to the base is a [NCERT Exemplar Problems]

(a) circle

(b) frustum of a cone

(c) sphere

(d) hemisphere

**Answer/ Explanation**

Answer: a

Explaination: (a) Circle.

35. A solid is hemispherical at the bottom and

conical (of same radius) above it. If the surface areas of the two parts are equal, then the ratio of its radius and the slant height of the conical part is ____ . [Foreign 2011]

**Answer/ Explanation**

Answer:

Explaination:

C.S.A of conical part = C.S.A. of spherical part

πrl = 2πr²

l = 2r

⇒ \(\frac{1}{2}\) = \(\frac{r}{l}\)

⇒ r : l = 1 : 2

36. Two cubes each with 6 cm edge are joined end to end. The surface area of the resulting cuboid is ____ .

**Answer/ Explanation**

Answer:

Explaination:

[360 cm²]

Hint: Length of resulting cuboid = 12 cm.

Width = 6 cm, height = 6 cm.

∴ Surface area

= 2(12 × 6 +12 × 6 + 6 × 6)

= 2(180) = 360 cm².

37. 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 4nrh + 4rcr2. [True/False] [NCERT Exemplar Problems]

**Answer/ Explanation**

Answer:

Explaination:

38. A cube of side 4 cm is cut into cubes of side 1 cm, then total surface area of all the small cubes is ______ .

**Answer/ Explanation**

Answer:

Explaination:

384 cm²

Volume of bigger cube = 4 × 4 × 4 = 64 cm^{3}

Volume of one smaller cube = 1 × 1 × 1 = 1 cm^{3}

Number of smaller cubes = \(\frac{64}{1}\) = 64

Surface area of one smaller cube = 6 × 1²

= 6 cm²

∴ Total surface area = 6 × 64 = 384 cm²

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

**Answer/ Explanation**

Answer:

Explaination:

[6 : π] Hint:

Let side of cube = x

Volume of cube = x^{3}

Diameter of sphere = x

40. A cube of side 6 cm is cut into a number of cubes, each of side 2 cm. The number of cubes will be ______ .

**Answer/ Explanation**

Answer:

Explaination: 27

41. Two cubes have their volumes in the ratio 1 : 27. Find the ratio of their surface areas. [CBSE 2018 (C)]

**Answer/ Explanation**

Answer:

Explaination:

42. A conical military tent having diameter of the base 24 m and slant height of the tent is 13 m, find the curved surface area of the cone. [π = \(\frac{22}{7}\)]

**Answer/ Explanation**

Answer:

Explaination:

43. Volume and surface area of a solid hemisphere are numerically equal. What is the diameter of hemisphere? [Delhi 2017]

**Answer/ Explanation**

Answer:

Explaination:

44. A joker’s cap is in the form of a right circular cone of base radius 7 cm and the slant height is 25 cm. Find the area of the cap. [π = \(\frac{22}{7}\)]

**Answer/ Explanation**

Answer:

Explaination:

Base radius of Joker’s cap = 7 cm;

slant height = 25 cm

Curved surface area = πrl = \(\frac{22}{7}\) × 7 × 25

= 550 cm²

45. A cylinder and a cone are of same base radius and of same height. Find the ratio of the volume of cylinder to that of the cone.

**Answer/ Explanation**

Answer:

Explaination:

46. Two cylindrical cans have equal base areas. If one of the can is 15 cm high and other is 20 cm high, find the ratio of their volumes.

**Answer/ Explanation**

Answer:

Explaination:

47. A sphere of maximum volume is cut out from a solid hemisphere of radius 7 cm. What is the ratio of the volume of the hemisphere to that of the cut out sphere?

**Answer/ Explanation**

Answer:

Explaination:

48. Three cubes of iron whose edges are 6 cm, 8 cm and 10 cm respectively are melted and formed into a single cube. The edge of the new cube formed is ____ .

**Answer/ Explanation**

Answer:

Explaination:

12 cm

Hint: 6^{3} + 8^{3} + 10^{3} = l^{3}

⇒ 216 + 512+ 1000 = l^{3}

⇒ 1728 = l^{3}

⇒ l = 12 cm.

49. A metal sheet 27 cm long, 8 cm broad and 1 cm thick is melted into a cube. The difference between surface areas of two solids is ____ .

**Answer/ Explanation**

Answer:

Explaination:

[286 cm²]

Hint: Surface area of the metal sheet

= 2 [27 × 8 + 8 × 1 +27 × 1]

= 2[216 + 35] = 502 cm²

Since this sheet is melted to form a cube, therefore,

Volume of cube = Volume of cuboid metal sheet

⇒ side^{3} = 27 × 8 × 1 cm^{3}

∴ side = \(\sqrt[3]{27 \times 8 \times 1}\) = 6 cm

∴ Surface area = 6 x 6² = 216 cm²

Difference = 502 – 216 = 286 cm².

50. A copper sphere of radius 3 cm is beaten and drawn into a wire of diameter 0.2 cm. The length of the wire is ___ .

**Answer/ Explanation**

Answer:

Explaination: 36 m

51. The dimensions of a metallic cuboid are 100 cm x 80 cm * 64 cm. It is melted and recast into a cube. Find the surface area of the cube.

**Answer/ Explanation**

Answer:

Explaination:

Dimensions of the metallic cuboid are

100 cm × 80 cm × 64 cm

100 × 80 × 64 = a3 (where a = side of cube)

⇒ 10 × 2 × 4 = a

⇒ a = 80cm

Surface area of the cube = 6a² = 6(80)²

= 6 × 80 × 80 = 38400 cm²

52. The slant height of the frustum of a cone is 5 cm. If the difference between the radii of its two circular ends is 4 cm, write the height of the frustum.

**Answer/ Explanation**

Answer:

Explaination:

53. A farmer wants to dig a well either in the form of a cuboid of dimension 1 m × 1 m and depth 7 m or in the form of a cylinder of diameter 1 m and depth 7 m. The rate of digging the well is ₹ 500/m^{3}. Find the cost to dig both the wells [π = \(\frac{22}{7}\)]

**Answer/ Explanation**

Answer:

Explaination:

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