Mensuration (Part-7)

11. The lateral surface area of a cone is 550 cm². If the diameter of the cone is 14 cm, then the height of the cone is: [Matriculation Level 20/06/2024 (Shift-1)]

(a) 24 cm
(b) 12.5 cm
(c) 12 cm
(d) 25 cm

Correct Answer: (a) 24 cm

Solution:

12. The radius of a hemisphere is 9 cm. Its volume will be: [Matriculation Level 20/06/2024 (Shift-4)]

(a) 712π cm³
(b) 243π cm³
(c) 486π cm³
(d) 972π cm³

Correct Answer: (c) 486π cm³

Solution:

13. If the cylinder height is 9 cm and the base area is 25π cm², then find the total surface area. [Matriculation Level 20/06/2024 (Shift-4)]

(a) 240 cm²
(b) 140 cm²
(c) 440 cm²
(d) 340 cm²

Correct Answer: (c) 440 cm²

Solution:

14. The height of one cone is 3 times the height of another cone, while its radius is half of the radius of the other cone. If their total volume is 100 unit³, then the difference in the volumes of the cones is______unit³. [Matriculation Level 21/06/2024 (Shift-1)]

(a) 12.5
(b) 14.3
(c) 13.4
(d) 15.5

Correct Answer: (b) 14.3

Solution:

15. A cube is having surface area of 5400 square units. Its volume would increase approximately if the _____ side is increased by 5 units. [Matriculation Level 21/06/2024 (Shift-1)]

(a) 59%
(b) 45%
(c) 55%
(d) 50%

Correct Answer: (a) 59%

Solution:

16. If the radius of a sphere is increased by 2 cm, its surface area increases by 704 cm². What was the radius of the sphere before the increase? (Use π = 22/7) [Matriculation Level 21/06/2024 (Shift-1)]

(a) 14 cm
(b) 11 cm
(c) 12 cm
(d) 13 cm

Correct Answer: (d) 13 cm

Solution:

17. What must be the total percentage change in the volume of a cuboid if its length and breadth are decreased by 10% and 20%, respectively, while its height is increased by 40%? [Matriculation Level 21/06/2024 (Shift-4)]

(a) 0.8% increase
(b) 0.8% decrease
(c) 1.8% increase
(d) 1.8% decrease

Correct Answer: (a) 0.8% increase

Solution:

18. There is a large cone with a diameter of 14 m and height of 12 m. It is being filled with water at a rate of 2 m³ in every 20 seconds. How long will it take to fill the cone? [Matriculation Level 21/06/2024 (Shift-4)]

(a) 313 sec
(b) 6160 sec
(c) 616 sec
(d) 12320 sec

Correct Answer: (b) 6160 sec

Solution:

19. The volume of a cuboid is twice the volume of a cube. If the dimensions of the cuboid are 12 cm, 16 cm and 18 cm, then the total surface area of the cube is: [Matriculation Level 21/06/2024 (Shift-4)]

(a) 625 cm²
(b) 864 cm²
(c) 484 cm²
(d) 764 cm²

Correct Answer: (b) 864 cm²

Solution:

20. The height of a solid cylinder is 4 times its radius. Its curved surface area is______times its base area. [Matriculation Level 21/06/2024 (Shift-4)]

(a) 2
(b) 6
(c) 8
(d) 4

Correct Answer: (c) 8

Solution:

Mensuration (Part-7)

11. The lateral surface area of a cone is 550 cm². If the diameter of the cone is 14 cm, then the height of the cone is: [Matriculation Level 20/06/2024 (Shift-1)]

12. The radius of a hemisphere is 9 cm. Its volume will be: [Matriculation Level 20/06/2024 (Shift-4)]

13. If the cylinder height is 9 cm and the base area is 25π cm², then find the total surface area. [Matriculation Level 20/06/2024 (Shift-4)]

14. The height of one cone is 3 times the height of another cone, while its radius is half of the radius of the other cone. If their total volume is 100 unit³, then the difference in the volumes of the cones is______unit³. [Matriculation Level 21/06/2024 (Shift-1)]

15. A cube is having surface area of 5400 square units. Its volume would increase approximately if the _____ side is increased by 5 units. [Matriculation Level 21/06/2024 (Shift-1)]

16. If the radius of a sphere is increased by 2 cm, its surface area increases by 704 cm². What was the radius of the sphere before the increase? (Use π = 22/7) [Matriculation Level 21/06/2024 (Shift-1)]

17. What must be the total percentage change in the volume of a cuboid if its length and breadth are decreased by 10% and 20%, respectively, while its height is increased by 40%? [Matriculation Level 21/06/2024 (Shift-4)]

18. There is a large cone with a diameter of 14 m and height of 12 m. It is being filled with water at a rate of 2 m³ in every 20 seconds. How long will it take to fill the cone? [Matriculation Level 21/06/2024 (Shift-4)]

19. The volume of a cuboid is twice the volume of a cube. If the dimensions of the cuboid are 12 cm, 16 cm and 18 cm, then the total surface area of the cube is: [Matriculation Level 21/06/2024 (Shift-4)]

20. The height of a solid cylinder is 4 times its radius. Its curved surface area is______times its base area. [Matriculation Level 21/06/2024 (Shift-4)]

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