12. Surface Areas and Volumes

*नोट: यह सेक्शन रिवीजन के लिए है। अपना ज्ञान परखने के लिए ऊपर दिए गए क्विज़ में भाग लें।

1. What is the formula for the volume of a cylinder with radius r and height h?
   A) pi r^2 h  |  B) 1/3 pi r^2 h  |  C) 2 pi r h  |  D) 2 pi r (r+h)
2. The curved surface area of a right circular cone of radius r and slant height l is?
   A) pi r^2  |  B) pi r l  |  C) 2 pi r l  |  D) pi r (r+l)
3. What is the total surface area of a solid hemisphere of radius r?
   A) 2 pi r^2  |  B) 3 pi r^2  |  C) 4 pi r^2  |  D) 2/3 pi r^3
4. What is the volume of a sphere of radius r?
   A) 4/3 pi r^3  |  B) 2/3 pi r^3  |  C) 4 pi r^2  |  D) 3 pi r^2
5. The surface area of a sphere of radius 14 cm is? (Use pi = 22/7)
   A) 2464 sq cm  |  B) 1232 sq cm  |  C) 616 sq cm  |  D) 4928 sq cm
6. If the radius of a cylinder is doubled and its height is halved, its volume will be?
   A) Halved  |  B) Doubled  |  C) Same  |  D) Quadrupled
7. What is the volume of a cone of radius 7 cm and height 12 cm? (Use pi = 22/7)
   A) 616 cubic cm  |  B) 1232 cubic cm  |  C) 1848 cubic cm  |  D) 308 cubic cm
8. The curved surface area of a cylinder of radius 7 cm and height 10 cm is?
   A) 440 sq cm  |  B) 220 sq cm  |  C) 880 sq cm  |  D) 154 sq cm
9. What is the slant height of a cone if its radius is 3 cm and height is 4 cm?
   A) 5 cm  |  B) 7 cm  |  C) 25 cm  |  D) 1 cm
10. A cylindrical pencil sharpened at one edge is the combination of?
    A) A cylinder and a cone  |  B) A cylinder and a hemisphere  |  C) Two cylinders  |  D) A cone and a hemisphere
11. A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to 1 cm and the height of the cone is equal to its radius. The volume of the solid in terms of pi is?
    A) pi cubic cm  |  B) 2pi cubic cm  |  C) 3pi cubic cm  |  D) 4pi cubic cm
12. A metallic sphere of radius 4.2 cm is melted and recast into the shape of a cylinder of radius 6 cm. The height of the cylinder is?
    A) 2.74 cm  |  B) 3.14 cm  |  C) 4.2 cm  |  D) 1.4 cm
13. The volume of two spheres are in the ratio 64:27. The ratio of their surface areas is?
    A) 3:4  |  B) 4:3  |  C) 9:16  |  D) 16:9
14. Two cubes each of volume 64 cubic cm are joined end to end. The surface area of the resulting cuboid is?
    A) 160 sq cm  |  B) 128 sq cm  |  C) 192 sq cm  |  D) 64 sq cm
15. A solid sphere of radius r is melted and cast into the shape of a solid cone of height r. The radius of the base of the cone is?
    A) r  |  B) 2r  |  C) 3r  |  D) 4r
16. If the volume of a cube is 1331 cubic cm, the length of its edge is?
    A) 11 cm  |  B) 12 cm  |  C) 13 cm  |  D) 9 cm
17. A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends. The length of the entire capsule is 14 mm and the diameter of the capsule is 5 mm. Its surface area is?
    A) 220 sq mm  |  B) 110 sq mm  |  C) 440 sq mm  |  D) 330 sq mm
18. A plumbline (sahul) is a combination of?
    A) A cone and a cylinder  |  B) A hemisphere and a cone  |  C) Frustum of a cone and cylinder  |  D) Sphere and cylinder
19. The ratio of the total surface area of a solid hemisphere to the square of its radius is?
    A) 2pi : 1  |  B) 3pi : 1  |  C) 4pi : 1  |  D) pi : 1
20. How many solid cylinders of radius 2 cm and height 3 cm can be made by melting a solid cylinder of radius 6 cm and height 12 cm?
    A) 36  |  B) 18  |  C) 9  |  D) 24
21. Water flows at the rate of 10 m/minute through a cylindrical pipe 5 mm in diameter. How long would it take to fill a conical vessel whose diameter at the base is 40 cm and depth 24 cm?
    A) 51.2 minutes  |  B) 25.6 minutes  |  C) 102.4 minutes  |  D) 45 minutes
22. A tent is in the shape of a cylinder surmounted by a conical top. If the height and diameter of the cylindrical part are 2.1 m and 4 m respectively, and the slant height of the top is 2.8 m, find the area of the canvas used.
    A) 44 sq m  |  B) 22 sq m  |  C) 88 sq m  |  D) 66 sq m
23. A hemispherical tank full of water is emptied by a pipe at the rate of 25/7 liters per second. How much time will it take to empty half the tank, if it is 3m in diameter?
    A) 16.5 minutes  |  B) 33 minutes  |  C) 10.5 minutes  |  D) 20 minutes
24. A wooden article was made by scooping out a hemisphere from each end of a solid cylinder. If the height of the cylinder is 10 cm, and its base is of radius 3.5 cm, find the total surface area.
    A) 374 sq cm  |  B) 400 sq cm  |  C) 220 sq cm  |  D) 154 sq cm
25. Spherical marbles of diameter 1.4 cm are dropped into a cylindrical beaker of diameter 7 cm containing some water. Find the number of marbles that should be dropped into the beaker so that the water level rises by 5.6 cm.
    A) 150  |  B) 200  |  C) 100  |  D) 50
26. A well of diameter 3m is dug 14m deep. The earth taken out of it has been spread evenly all around it in the shape of a circular ring of width 4m to form an embankment. Find the height of the embankment.
    A) 1.125 m  |  B) 2.25 m  |  C) 1.5 m  |  D) 0.5 m
27. Water in a canal, 6m wide and 1.5m deep, is flowing with a speed of 10 km/h. How much area will it irrigate in 30 minutes, if 8 cm of standing water is needed?
    A) 562500 sq m  |  B) 450000 sq m  |  C) 56250 sq m  |  D) 112500 sq m
28. A right circular cone of radius 3 cm and height 4 cm is made of solid metal. It is melted and recast into a sphere. What is the radius of the sphere?
    A) Cube root of 9 cm  |  B) 2 cm  |  C) 3 cm  |  D) Cube root of 12 cm
29. A solid metallic sphere of radius 10.5 cm is melted and recast into a number of smaller cones, each of radius 3.5 cm and height 3 cm. Find the number of cones so formed.
    A) 126  |  B) 130  |  C) 112  |  D) 140
30. The curved surface area of a right circular cylinder is 4.4 sq m. If the radius of the base of the cylinder is 0.7 m, find its height.
    A) 1 m  |  B) 2 m  |  C) 0.5 m  |  D) 1.5 m