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Question (21)

QN0037041

21. A cylinder has radius 7 cm and height 10 cm. A cone of radius 7 cm is placed on its top. Which surfaces are included in the external surface area?

(A) CSA of cylinder + CSA of cone + lower circular base of cylinder
(B) TSA of cylinder + TSA of cone
(C) Only CSA of both solids
(D) Only the circular bases

Correct Answer: A

Explanation:

The common circular face is hidden. The exposed surfaces are the curved surfaces plus the bottom circular base.

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Question (22)

QN0037042

22. A rocket consists of a cylinder of radius 3 cm and height 20 cm with a cone of the same radius and height 4 cm mounted on it. If the cone's slant height is 5 cm, the external area excluding the common circular face is:

(A) 132π cm²
(B) 144π cm²
(C) 150π cm²
(D) 162π cm²

Correct Answer: B

Explanation:

CSA of cylinder = 120π. CSA of cone = 15π. Bottom base = 9π. Total = 144π cm².

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Question (23)

QN0037043

23. A cubical block of side 5 cm has a hemisphere of diameter 4 cm fixed on its top. Using π = 22/7, the total external surface area is:

(A) 150 cm²
(B) 156.86 cm²
(C) 163.86 cm²
(D) 170.28 cm²

Correct Answer: C

Explanation:

TSA = TSA of cube − base area of hemisphere + CSA of hemisphere = 150 + πr² = 150 + 13.86 = 163.86 cm².

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Question (24)

QN0037044

24. A cone is mounted on a cylinder. The cone has a larger base radius than the cylinder. Which additional area of the cone's base remains exposed?

(A) A circular disc
(B) A ring-shaped region
(C) A hemisphere
(D) A semicircle

Correct Answer: B

Explanation:

The smaller circular base of the cylinder covers only part of the larger circular base of the cone, leaving a ring exposed.

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Question (25)

QN0037045

25. A cone has radius 2.5 cm and slant height 6.5 cm. A cylinder below it has radius 1.5 cm. The exposed ring area at the junction is:

(A) 2π cm²
(B) 4π cm²
(C) 6.25π cm²
(D) 8π cm²

Correct Answer: B

Explanation:

Ring area = π(2.5² − 1.5²) = π(6.25 − 2.25) = 4π cm².

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Question (26)

QN0037046

26. When two solids are joined, their surface areas cannot simply be added because:

(A) Their volumes change
(B) Some surfaces become internal
(C) Their radii always change
(D) Their heights become zero

Correct Answer: B

Explanation:

The surfaces at the joining region are no longer exposed.

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Question (27)

QN0037047

27. When two solids are joined without overlap, their combined volume is:

(A) Difference of their volumes
(B) Product of their volumes
(C) Sum of their volumes
(D) Average of their volumes

Correct Answer: C

Explanation:

The volume of a combined solid is the sum of the volumes of its constituent solids.

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Question (28)

QN0037048

28. A shed is formed by a cuboid of dimensions 15 m × 7 m × 8 m surmounted by a half-cylinder of diameter 7 m and length 15 m. Its volume is:

(A) 840 m³
(B) 1050 m³
(C) 1128.75 m³
(D) 1275 m³

Correct Answer: C

Explanation:

Cuboid volume = 15 × 7 × 8 = 840 m³. Half-cylinder volume = 1/2 × 22/7 × 3.5² × 15 = 288.75 m³. Total = 1128.75 m³.

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Question (29)

QN0037049

29. The shed in Question 28 contains machinery occupying 300 m³ and 20 workers occupying 0.08 m³ each. The volume of air remaining is:

(A) 825.55 m³
(B) 827.15 m³
(C) 828.75 m³
(D) 830.15 m³

Correct Answer: B

Explanation:

Workers occupy 20 × 0.08 = 1.6 m³. Air = 1128.75 − 300 − 1.6 = 827.15 m³.

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Question (30)

QN0037050

30. A cylindrical glass has internal radius 2.5 cm and height 10 cm. Its apparent capacity is:

(A) 157 cm³
(B) 196.25 cm³
(C) 225.50 cm³
(D) 245 cm³

Correct Answer: B

Explanation:

Apparent volume = πr²h = 3.14 × 2.5² × 10 = 196.25 cm³.

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Question (21)

21. A cylinder has radius 7 cm and height 10 cm. A cone of radius 7 cm is placed on its top. Which surfaces are included in the external surface area?

Explanation:

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Question (22)

22. A rocket consists of a cylinder of radius 3 cm and height 20 cm with a cone of the same radius and height 4 cm mounted on it. If the cone's slant height is 5 cm, the external area excluding the common circular face is:

Explanation:

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Question (23)

23. A cubical block of side 5 cm has a hemisphere of diameter 4 cm fixed on its top. Using π = 22/7, the total external surface area is:

Explanation:

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Question (24)

24. A cone is mounted on a cylinder. The cone has a larger base radius than the cylinder. Which additional area of the cone's base remains exposed?

Explanation:

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Question (25)

25. A cone has radius 2.5 cm and slant height 6.5 cm. A cylinder below it has radius 1.5 cm. The exposed ring area at the junction is:

Explanation:

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Question (26)

26. When two solids are joined, their surface areas cannot simply be added because:

Explanation:

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Question (27)

27. When two solids are joined without overlap, their combined volume is:

Explanation:

Link:

Question (28)

28. A shed is formed by a cuboid of dimensions 15 m × 7 m × 8 m surmounted by a half-cylinder of diameter 7 m and length 15 m. Its volume is:

Explanation:

Link:

Question (29)

29. The shed in Question 28 contains machinery occupying 300 m³ and 20 workers occupying 0.08 m³ each. The volume of air remaining is:

Explanation:

Link:

Question (30)

30. A cylindrical glass has internal radius 2.5 cm and height 10 cm. Its apparent capacity is:

Explanation:

Link:

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