Mensuration (Part-3)

11. The volume of the hemisphere is 486 cm³. If the radius is tripled, then what will be its curved surface area (in cm²) ? [SSC MTS 07/10/2024 (Afternoon)]

(a) 1458
(b) 1025π
(c) 1458π
(d) 1546

Correct Answer: (c) 1458π

Solution:

12. A hemispherical bowl of internal radius 15 cm contains a liquid. The liquid is to be filled into cylindrical shaped bottles of diameter 5 cm and height 6 cm. The number of bottles required to empty the bowl is: [SSC MTS 08/10/2024 (Morning)]

(a) 40
(b) 30
(c) 60
(d) 50

Correct Answer: (c) 60

Solution:

13. A solid cone of base radius 7 cm and height 18 cm is melted and recast into a hollow metal hemisphere of internal and external radii 20 cm and R cm, respectively. What is the value of R (in cm)? [SSC MTS 08/10/2024 (Afternoon)]

Correct Answer: (b)

Solution:

14. A solid spherical item is melted into the shape of a cylinder mounted by a cone having same radius. The diameters of the cylinder and sphere are 21 cm each. What is the height (in cm) of the cone if the height of the cylinder is 7 cm? (Take π = 22/7) [SSC MTS 08/10/2024 (Evening)]

(a) 21
(b) 10.5
(c) 14
(d) 7

Correct Answer: (a) 21

Solution:

15. ABCDEF is a regular hexagon, and m (AD) 12 cm. What is the area (in cm²) of the given hexagon ? [SSC MTS 09/10/2024 (Morning)]

(a) 216√3
(b) 54√3
(c) 108√3
(d) 162√3

Correct Answer: (b) 54√3

Solution:

16. A right circular cone of height h and radius R is cut by a parallel to the base at a distance h/5 from the base. The 5 ratio of the curved surface area of the frustum and total surface area of the resulting cone is: [SSC MTS 09/10/2024 (Afternoon)]

(a) 16 (R+L) : 9L
(b) 9 (R+L) : 16L
(c) 16L : 9 (R+L)
(d) 9L : 16 (R+L)

Correct Answer: (d) 9L : 16 (R+L)

Solution:

17. The radius of the base and height of a right circular cone are in the ratio 8:15. Find the slant height of the cone if its volume is (10057)5/7 cm³ [SSC MTS 09/10/2024 (Afternoon)]

(a) 12 cm
(b) 17 cm
(c) 21 cm
(d) 15 cm

Correct Answer: (b) 17 cm

Solution:

18. A rectangular sheet of length 28 cm and breadth 16 cm is folded to meet the edges so that it is made into a cylindrical pipe in two possible ways one along the length and the other along the breadth. The larger volume is how much percentage of smaller volume ? [SSC MTS 09/10/2024 (Evening)]

(a) 165%
(b) 180%
(c) 185%
(d) 175%

Correct Answer: (d) 175%

Solution:

19. A conical tent is to accommodate 12 persons. Each person must have 5 m² of the space on the ground and 20 m³ of air to breathe. The height of the tent should be: [SSC MTS 09/10/2024 (Evening)]

(a) 12m
(b) 13m
(c) 12.5m
(d) 22 m

Correct Answer: (a) 12m

Solution:

20. A medicine capsule is shaped like a cylinder with two hemispheres attached to each of its ends. The length of the entire capsule is 15 mm, and its diameter is 6 mm. Calculate the surface area (in mm² rounded to the nearest integer) of the capsule. (Use π = 22/7)) [SSC MTS 14/10/2024 (Afternoon)]

(a) 286
(b) 283
(c) 289
(d) 280

Correct Answer: (b) 283

Solution:

Mensuration (Part-3)

11. The volume of the hemisphere is 486 cm³. If the radius is tripled, then what will be its curved surface area (in cm²) ? [SSC MTS 07/10/2024 (Afternoon)]

12. A hemispherical bowl of internal radius 15 cm contains a liquid. The liquid is to be filled into cylindrical shaped bottles of diameter 5 cm and height 6 cm. The number of bottles required to empty the bowl is: [SSC MTS 08/10/2024 (Morning)]

13. A solid cone of base radius 7 cm and height 18 cm is melted and recast into a hollow metal hemisphere of internal and external radii 20 cm and R cm, respectively. What is the value of R (in cm)? [SSC MTS 08/10/2024 (Afternoon)]

14. A solid spherical item is melted into the shape of a cylinder mounted by a cone having same radius. The diameters of the cylinder and sphere are 21 cm each. What is the height (in cm) of the cone if the height of the cylinder is 7 cm? (Take π = 22/7) [SSC MTS 08/10/2024 (Evening)]

15. ABCDEF is a regular hexagon, and m (AD) 12 cm. What is the area (in cm²) of the given hexagon ? [SSC MTS 09/10/2024 (Morning)]

16. A right circular cone of height h and radius R is cut by a parallel to the base at a distance h/5 from the base. The 5 ratio of the curved surface area of the frustum and total surface area of the resulting cone is: [SSC MTS 09/10/2024 (Afternoon)]

17. The radius of the base and height of a right circular cone are in the ratio 8:15. Find the slant height of the cone if its volume is (10057)5/7 cm³ [SSC MTS 09/10/2024 (Afternoon)]

18. A rectangular sheet of length 28 cm and breadth 16 cm is folded to meet the edges so that it is made into a cylindrical pipe in two possible ways one along the length and the other along the breadth. The larger volume is how much percentage of smaller volume ? [SSC MTS 09/10/2024 (Evening)]

19. A conical tent is to accommodate 12 persons. Each person must have 5 m² of the space on the ground and 20 m³ of air to breathe. The height of the tent should be: [SSC MTS 09/10/2024 (Evening)]

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