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Question (41)

QN0037061

41. For the tent in Question 40, if canvas costs ₹500 per m², the approximate cost is:

(A) ₹18,000
(B) ₹20,000
(C) ₹22,000
(D) ₹25,000

Correct Answer: C

Explanation:

Canvas area = 44 m². Cost = 44 × 500 = ₹22,000.

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Question (42)

QN0037062

42. A cylindrical vessel has radius 5 cm and height 8 cm. A hemispherical cavity of radius 5 cm is cut from one end. The volume removed by the cavity is:

(A) 125π/3 cm³
(B) 250π/3 cm³
(C) 500π/3 cm³
(D) 750π/3 cm³

Correct Answer: B

Explanation:

Volume of hemisphere = 2/3πr³ = 2/3π × 125 = 250π/3 cm³.

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Question (43)

QN0037063

43. A cone-shaped vessel has height 8 cm and radius 5 cm. Its capacity is:

(A) 100π/3 cm³
(B) 150π/3 cm³
(C) 200π/3 cm³
(D) 250π/3 cm³

Correct Answer: C

Explanation:

Volume = 1/3πr²h = 1/3π × 25 × 8 = 200π/3 cm³.

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Question (44)

QN0037064

44. Lead shots of radius 0.5 cm are dropped into a completely filled vessel. If one-fourth of the water flows out, the volume of displaced water is equal to:

(A) Volume of one lead shot
(B) Total volume of all lead shots
(C) Half the volume of all lead shots
(D) Twice the volume of all lead shots

Correct Answer: B

Explanation:

The volume of water displaced equals the volume occupied by the submerged lead shots.

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Question (45)

QN0037065

45. A spherical glass vessel has a cylindrical neck. To calculate its capacity, which volumes should be combined?

(A) Only the spherical part
(B) Only the cylindrical neck
(C) Volume of spherical part and cylindrical neck
(D) Difference between spherical and cylindrical volumes

Correct Answer: C

Explanation:

The vessel consists of a spherical portion and a cylindrical neck, so their volumes are added.

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Question (46)

QN0037066

46. A solid iron pole consists of a cylinder of height 220 cm and diameter 24 cm, surmounted by a cylinder of height 60 cm and radius 8 cm. The radius of the lower cylinder is:

(A) 6 cm
(B) 8 cm
(C) 12 cm
(D) 24 cm

Correct Answer: C

Explanation:

Radius = diameter/2 = 24/2 = 12 cm.

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Question (47)

QN0037067

47. For the iron pole in Question 46, using π = 3.14, the volume of the lower cylinder is:

(A) 99440 cm³
(B) 99475.2 cm³
(C) 100000 cm³
(D) 101376 cm³

Correct Answer: B

Explanation:

Volume = πr²h = 3.14 × 12² × 220 = 99475.2 cm³.

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Question (48)

QN0037068

48. A solid consisting of a cone of radius 60 cm and height 120 cm standing on a hemisphere of radius 60 cm is placed in a cylinder of radius 60 cm and height 180 cm. The volume of water left is:

(A) 678240 cm³
(B) 813888 cm³
(C) 1017360 cm³
(D) 1220832 cm³

Correct Answer: B

Explanation:

Cylinder volume = π × 60² × 180. Solid volume = cone volume + hemisphere volume. Subtracting the solid volume from the cylinder volume gives approximately 813888 cm³ using π = 22/7.

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Question (49)

QN0037069

49. A pen stand is a cuboid of dimensions 15 cm × 10 cm × 3.5 cm with four conical depressions. Each depression has radius 0.5 cm and depth 1.4 cm. The volume of wood removed from the four depressions is:

(A) 1.47 cm³
(B) 1.67 cm³
(C) 2.47 cm³
(D) 3.14 cm³

Correct Answer: A

Explanation:

One depression volume = 1/3 × 22/7 × 0.5² × 1.4 ≈ 0.3667 cm³. Four depressions ≈ 1.47 cm³.

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Question (50)

QN0037070

50. A solid is formed by joining a cone and a hemisphere of the same radius. Which statement correctly describes the calculation of its volume and external surface area?

(A) Both are obtained by simply adding the TSA of the two solids
(B) Volume is the sum of constituent volumes, while the common joining surface is excluded from external surface area
(C) Volume is the difference of constituent volumes, while all surfaces are included
(D) Both volume and surface area are calculated by adding only the curved surfaces

Correct Answer: B

Explanation:

When solids are joined, their volumes are added, but the common joining surface is internal and is not counted in the external surface area.

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Question (41)

41. For the tent in Question 40, if canvas costs ₹500 per m², the approximate cost is:

Explanation:

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Question (42)

42. A cylindrical vessel has radius 5 cm and height 8 cm. A hemispherical cavity of radius 5 cm is cut from one end. The volume removed by the cavity is:

Explanation:

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Question (43)

43. A cone-shaped vessel has height 8 cm and radius 5 cm. Its capacity is:

Explanation:

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Question (44)

44. Lead shots of radius 0.5 cm are dropped into a completely filled vessel. If one-fourth of the water flows out, the volume of displaced water is equal to:

Explanation:

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Question (45)

45. A spherical glass vessel has a cylindrical neck. To calculate its capacity, which volumes should be combined?

Explanation:

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Question (46)

46. A solid iron pole consists of a cylinder of height 220 cm and diameter 24 cm, surmounted by a cylinder of height 60 cm and radius 8 cm. The radius of the lower cylinder is:

Explanation:

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Question (47)

47. For the iron pole in Question 46, using π = 3.14, the volume of the lower cylinder is:

Explanation:

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Question (48)

48. A solid consisting of a cone of radius 60 cm and height 120 cm standing on a hemisphere of radius 60 cm is placed in a cylinder of radius 60 cm and height 180 cm. The volume of water left is:

Explanation:

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Question (49)

49. A pen stand is a cuboid of dimensions 15 cm × 10 cm × 3.5 cm with four conical depressions. Each depression has radius 0.5 cm and depth 1.4 cm. The volume of wood removed from the four depressions is:

Explanation:

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Question (50)

50. A solid is formed by joining a cone and a hemisphere of the same radius. Which statement correctly describes the calculation of its volume and external surface area?

Explanation:

Link:

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