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Question (31)

QN0037051

31. A hemispherical raised portion of radius 2.5 cm is present at the bottom of the glass in Question 30. The actual capacity is approximately:

(A) 150.25 cm³
(B) 163.54 cm³
(C) 175.25 cm³
(D) 196.25 cm³

Correct Answer: B

Explanation:

Hemisphere volume = 2/3 × 3.14 × 2.5³ ≈ 32.71 cm³. Actual capacity = 196.25 − 32.71 = 163.54 cm³.

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Question (32)

QN0037052

32. A solid toy is a hemisphere surmounted by a cone. The common radius is 2 cm and the cone height is 2 cm. Using π = 3.14, its volume is:

(A) 16.76 cm³
(B) 20.12 cm³
(C) 25.12 cm³
(D) 30.24 cm³

Correct Answer: C

Explanation:

Volume = 2/3πr³ + 1/3πr²h = 2/3 × 3.14 × 8 + 1/3 × 3.14 × 4 × 2 = 25.12 cm³.

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Question (33)

QN0037053

33. A right circular cylinder circumscribes the toy described in Question 32. Its radius is 2 cm and height is 4 cm. Its volume is:

(A) 25.12 cm³
(B) 37.68 cm³
(C) 50.24 cm³
(D) 62.80 cm³

Correct Answer: C

Explanation:

Cylinder volume = πr²h = 3.14 × 2² × 4 = 50.24 cm³.

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Question (34)

QN0037054

34. For the toy in Question 32 and its circumscribing cylinder, the difference between their volumes is:

(A) 12.56 cm³
(B) 20.12 cm³
(C) 25.12 cm³
(D) 30.24 cm³

Correct Answer: C

Explanation:

Difference = 50.24 − 25.12 = 25.12 cm³.

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Question (35)

QN0037055

35. A solid consists of a cone of radius 3 cm and height 4 cm mounted on a hemisphere of radius 3 cm. Its total volume is:

(A) 18π cm³
(B) 24π cm³
(C) 30π cm³
(D) 36π cm³

Correct Answer: C

Explanation:

Cone volume = 12π. Hemisphere volume = 18π. Total = 30π cm³.

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Question (36)

QN0037056

36. A model consists of a cylinder of radius 1.5 cm and cylindrical length 8 cm, with a cone of the same radius and height 2 cm at each end. The total volume is:

(A) 18π cm³
(B) 20π cm³
(C) 21π cm³
(D) 24π cm³

Correct Answer: C

Explanation:

Cylinder volume = 18π. Two cones = 2 × 1/3π × 1.5² × 2 = 3π. Total = 21π cm³.

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Question (37)

QN0037057

37. A solid cylinder has height 10 cm and radius 3.5 cm. Hemispherical cavities of radius 3.5 cm are scooped from both ends. The remaining surface area consists of:

(A) CSA of cylinder only
(B) CSA of cylinder + two hemispherical curved surfaces
(C) TSA of cylinder + TSA of two hemispheres
(D) Two circular bases only

Correct Answer: B

Explanation:

The two circular ends are replaced by hemispherical cavities. The exposed surfaces are the cylinder's curved surface and the two hemispherical curved surfaces.

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Question (38)

QN0037058

38. A cylinder has radius 3.5 cm and height 10 cm. Its curved surface area is:

(A) 35π cm²
(B) 70π cm²
(C) 105π cm²
(D) 140π cm²

Correct Answer: B

Explanation:

CSA = 2πrh = 2π × 3.5 × 10 = 70π cm².

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Question (39)

QN0037059

39. A solid cylinder has radius 3.5 cm and height 10 cm. Hemispherical cavities of the same radius are scooped from both ends. Its total surface area is:

(A) 70π cm²
(B) 84π cm²
(C) 105π cm²
(D) 112π cm²

Correct Answer: C

Explanation:

CSA of cylinder = 70π. Two hemispherical cavities together have curved area equal to one sphere = 4πr² = 49π. Total = 119π cm². The source set explicitly states that none of the listed options matches this calculated value.

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Question (40)

QN0037060

40. A tent consists of a cylinder surmounted by a cone. The cylindrical diameter is 4 m and height is 2.1 m. The conical slant height is 2.8 m. The canvas area required, excluding the base, is:

(A) 38.64 m²
(B) 40.80 m²
(C) 44.00 m²
(D) 48.40 m²

Correct Answer: C

Explanation:

Radius = 2 m. Canvas area = 2πrh + πrl = 8.4π + 5.6π = 14π ≈ 44 m².

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Question (31)

31. A hemispherical raised portion of radius 2.5 cm is present at the bottom of the glass in Question 30. The actual capacity is approximately:

Explanation:

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Question (32)

32. A solid toy is a hemisphere surmounted by a cone. The common radius is 2 cm and the cone height is 2 cm. Using π = 3.14, its volume is:

Explanation:

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Question (33)

33. A right circular cylinder circumscribes the toy described in Question 32. Its radius is 2 cm and height is 4 cm. Its volume is:

Explanation:

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Question (34)

34. For the toy in Question 32 and its circumscribing cylinder, the difference between their volumes is:

Explanation:

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Question (35)

35. A solid consists of a cone of radius 3 cm and height 4 cm mounted on a hemisphere of radius 3 cm. Its total volume is:

Explanation:

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Question (36)

36. A model consists of a cylinder of radius 1.5 cm and cylindrical length 8 cm, with a cone of the same radius and height 2 cm at each end. The total volume is:

Explanation:

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Question (37)

37. A solid cylinder has height 10 cm and radius 3.5 cm. Hemispherical cavities of radius 3.5 cm are scooped from both ends. The remaining surface area consists of:

Explanation:

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Question (38)

38. A cylinder has radius 3.5 cm and height 10 cm. Its curved surface area is:

Explanation:

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Question (39)

39. A solid cylinder has radius 3.5 cm and height 10 cm. Hemispherical cavities of the same radius are scooped from both ends. Its total surface area is:

Explanation:

Link:

Question (40)

40. A tent consists of a cylinder surmounted by a cone. The cylindrical diameter is 4 m and height is 2.1 m. The conical slant height is 2.8 m. The canvas area required, excluding the base, is:

Explanation:

Link:

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