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Question (11)

QN0037031

11. A cone has radius 3 cm and height 4 cm. Its slant height is:

(A) 4 cm
(B) 5 cm
(C) 6 cm
(D) 7 cm

Correct Answer: B

Explanation:

l = √(r² + h²) = √(9 + 16) = 5 cm.

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Question (12)

QN0037032

12. A cone of radius 7 cm and height 24 cm is joined to a hemisphere of radius 7 cm. The slant height of the cone is:

(A) 24 cm
(B) 25 cm
(C) 26 cm
(D) 31 cm

Correct Answer: B

Explanation:

l = √(7² + 24²) = √625 = 25 cm.

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Question (13)

QN0037033

13. A cone and hemisphere have the same radius. If the cone has height equal to its radius r, the volume of the combined solid is:

(A) 4/3 πr³
(B) 5/3 πr³
(C) 2πr³
(D) 7/3 πr³

Correct Answer: B

Explanation:

Cone volume = 1/3πr³ and hemisphere volume = 2/3πr³. Total = πr³. The source set's stated answer does not match its calculation; therefore the mathematically calculated value is πr³, which is not among the options.

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Question (14)

QN0037034

14. A solid is made by joining a cone of radius 3.5 cm and height 12 cm to a hemisphere of the same radius. The common circular face is:

(A) Included in the external surface area
(B) Excluded from the external surface area
(C) Counted twice
(D) Equal to the curved surface of the cone

Correct Answer: B

Explanation:

The common face becomes internal after joining the two solids.

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Question (15)

QN0037035

15. A toy is made by placing a cone on a hemisphere. The radius of both is 3.5 cm and the total height is 15.5 cm. The height of the cone is:

(A) 10 cm
(B) 12 cm
(C) 15.5 cm
(D) 19 cm

Correct Answer: B

Explanation:

Height of hemisphere = radius = 3.5 cm. Cone height = 15.5 − 3.5 = 12 cm.

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Question (16)

QN0037036

16. For the toy in Question 15, the slant height of the cone is:

(A) 10.5 cm
(B) 11 cm
(C) 12.5 cm
(D) 13 cm

Correct Answer: C

Explanation:

l = √(12² + 3.5²) = √156.25 = 12.5 cm.

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Question (17)

QN0037037

17. A cylinder of radius 7 cm and height 10 cm has a hemispherical depression of the same radius at one end. The external surface area consists of:

(A) CSA of cylinder + CSA of hemisphere + one circular base
(B) TSA of cylinder + TSA of hemisphere
(C) CSA of cylinder only
(D) CSA of hemisphere only

Correct Answer: A

Explanation:

The exposed surfaces are the curved cylindrical surface, curved hemispherical depression, and the opposite circular base.

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Question (18)

QN0037038

18. A bird-bath consists of a cylinder of radius 30 cm and height 1.45 m with a hemispherical depression at one end. Using π = 22/7, its total surface area is:

(A) 2.2 m²
(B) 3.3 m²
(C) 4.4 m²
(D) 5.5 m²

Correct Answer: B

Explanation:

Convert height to 145 cm. TSA = 2πrh + 2πr² = 2πr(h+r) = 33000 cm² = 3.3 m².

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Question (19)

QN0037039

19. A cylinder has radius 5 cm and height 12 cm. Its curved surface area is:

(A) 60π cm²
(B) 100π cm²
(C) 120π cm²
(D) 170π cm²

Correct Answer: C

Explanation:

CSA = 2πrh = 2π × 5 × 12 = 120π cm².

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Question (20)

QN0037040

20. A cone has radius 7 cm and slant height 10 cm. Its curved surface area is:

(A) 35π cm²
(B) 70π cm²
(C) 140π cm²
(D) 490π cm²

Correct Answer: B

Explanation:

CSA = πrl = π × 7 × 10 = 70π cm².

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Question (11)

11. A cone has radius 3 cm and height 4 cm. Its slant height is:

Explanation:

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Question (12)

12. A cone of radius 7 cm and height 24 cm is joined to a hemisphere of radius 7 cm. The slant height of the cone is:

Explanation:

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Question (13)

13. A cone and hemisphere have the same radius. If the cone has height equal to its radius r, the volume of the combined solid is:

Explanation:

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Question (14)

14. A solid is made by joining a cone of radius 3.5 cm and height 12 cm to a hemisphere of the same radius. The common circular face is:

Explanation:

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Question (15)

15. A toy is made by placing a cone on a hemisphere. The radius of both is 3.5 cm and the total height is 15.5 cm. The height of the cone is:

Explanation:

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Question (16)

16. For the toy in Question 15, the slant height of the cone is:

Explanation:

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Question (17)

17. A cylinder of radius 7 cm and height 10 cm has a hemispherical depression of the same radius at one end. The external surface area consists of:

Explanation:

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Question (18)

18. A bird-bath consists of a cylinder of radius 30 cm and height 1.45 m with a hemispherical depression at one end. Using π = 22/7, its total surface area is:

Explanation:

Link:

Question (19)

19. A cylinder has radius 5 cm and height 12 cm. Its curved surface area is:

Explanation:

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Question (20)

20. A cone has radius 7 cm and slant height 10 cm. Its curved surface area is:

Explanation:

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