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Q1. A cylindrical vessel of diameter 42 cm and height 40 cm contains water up to a depth of 16 cm. Now a solid iron cylinder, with diameter 14 cm and height 32 cm is placed upright in the cylindrical vessel. The volume of the water required to just submerge the solid cylinder will be
14, 000 cm3
15, 600 cm3
16, 045 cm3
17, 248 cm3
Q2. A circular tent is cylinder to a height of 4 m and conical above it. If its diameter is 105 m and its slant height is 40 m, then the area of canvas required is
1760 m2
2640 m2
3960 m2
7920 m2
Q3. An iron ball of radius 10.5 cm is melted and recast into small cones, each of radius 3.5 cm and height 3 cm. The number of cones is
150
126
100
140
Q4. The slant height of the frustum of a cone is 6 cm and the perimeter of its circular ends are 20 cm and 8 cm. Its curved surface area is
48 cm2
84 cm2
90 cm2
54 cm2
Q5. A cylinder and a cone are of the same base radius, but the height of the cone is four times that of the cylinder. The ratio of the volume of the cylinder to that of the cone is 
1:2
3:2
3:5
3:4
Q6. The radius of a cylindrical tank is 28 m. If its capacity is equal to that of a rectangular tank of size 28 m x16 m x 11 m, then its depth is 
2 m
3 m
4 m
5 m
Q7. A river 3 m deep and 10 m wide is flowing at the rate of 2 km per hour. How much water will fall into the sea in a minute?
1000 l
1000 kl
100 kl
10 kl
Q8. A cylinder whose height is two thirds of its diameter has the same volume as a sphere of radius 4 cm. The radius of the base of the cylinder will be
5 cm
4 cm
8 cm
2 cm
Q9. If a solid right circular cone of height 24 cm and base radius 6 cm is melted and recast in the shape of a sphere, then the radius of the sphere is
6 cm
4 cm
8 cm
12 cm
Q10. A frustum of a right circular cone has a diameter of base 20 cm, of top 12 cm, and height 3 cm. the area of the whole surface is
678.85 cm2
628.75 cm2
548.45 cm2
338.35 cm2
Q11. There are two cones. The curved surface area of one is twice that of the other. The slant height of the latter is twice that of the former. The ratio of their radii is
2:1
1:3
4:1
2:5
Q12. A cylinder and a cone are of the same base radius, but the height of the cone is double that of the cylinder. The ratio of the volume of the cylinder to that of the cone is
1:2
3:2
3:5
3:4
Q13. A golf ball has diameter equal to 4.2 cm. Its surface has 200 dimples each of radius 2 mm. Assuming that the dimples are hemispherical, total surface area which is exposed to the surroundings is
100 cm2
90 cm2
80.58 cm2
85.82 cm2
Q14. A shuttle cock used for playing badminton has the shape of the combination of :
A cylinder and a sphere
A sphere and a cone
A cylinder and a hemisphere
A hemisphere and frustum cone
Q15. The radius (in cm) of the largest right circular cone that can be cut out from a cube of edge 4.2 cm    is  
4.2
2.1
8.4
1.05
Q16. Radii of the cylinder and sphere are the same, and the height of the cylinder is twice its radius. Find the ratio of the volume of the cylinder to the sphere.
1:2
3:2
3:5
3:4
Q17. Haneef is processing sugarcane juice to make molasses, which is poured into moulds in the shape of a frustum of a cone having the diameters of the two circular faces as 30 cm and 35 cm and the vertical height of the mould is 14 cm. If each cm3 of molasses has a mass of about 1.2 g then the mass of the molasses that can be poured into each mould will be about
30 kg
20 g
15 kg
14 kg
Q18. The material of a cone is converted into the shape of a cylinder of equal radius. If the height of the cylinder is 5 cm, then the height of the cone is
10 cm
15 cm
18 cm
24 cm
Q19. A solid toy is in the form of a right circular cylinder with a hemispherical shape at one end and a cone at the other end. Their common diameter is 4.2 cm and the heights of the cylindrical and conical portions are 12 cm and 7 cm respectively. The approximate volume of the toy will be
300 cm3
200 cm3
218 cm3
250 cm3
Q20. A cylinder whose height is 4/3 of its radius has the same volume as a sphere of radius 8 cm. The radius of the base of the cylinder will be
5 cm
4 cm
8 cm
2 cm
Q21. 2 cubes of volume 64 cm3 are joined end to end. Find the surface area of resulting cuboid.
160  cm2
80 cm2
64 cm2
128 cm2
Q22. A cylindrical pencil sharpened at one edge is the combination of
A cone and a cylinder
Frustum of a cone and a cylinder
A hemisphere and a cylinder
Two cylinders
Q23. The radii of two right circular cylinders are in the ratio 2: 3 and their heights are in the ratio 5: 4. The ratio of their volumes will be
6: 7
5: 9
2: 3
4: 3
Q24. If two identical solid cubes each of volume 64 cm3 are joined end to end, then the total surface area of the resulting cuboid is:
160 cm2
180 cm2
200 cm2
210 cm2
Q25. A container is in the form of a hemispherical bowl mounted by a hollow cylinder. The diameter of the sphere is 24 cm and the total height of the container is 16 cm. Its capacity is
5100 cm3
5390.60 cm3
5400 cm3
5425.92 cm3
Q26. An open container made up of a metal sheet is in the form of a frustum of a cone of height 8 cm with radii of its lower and upper ends as 4 cm and 10 cm respectively. The cost of the oil at the rate of Rs. 50 per litre, which can completely fill the container, will be
Rs. 45.60
Rs.65.50
Rs.70
Rs. 76.50
Q27. A circular cylinder shaped container having diameter 24 cm and height 10 cm is full of ice-cream. The ice-cream is to be filled into cones of height 8 cm and diameter 4 cm, having a hemispherical shape on the top. The number of such cones which can be filled with ice-cream is
70
80
90
100
Q28. The diameter of a sphere is 9 cm. It is melted and drawn into a wire of diameter 9 mm. The length of the wire is
6 mm
6 cm
6 m
6 km
Q29. The number of lead balls each of radius 1 cm, that can be formed from a sphere of radius 8 cm will be
400
225
512
380
Q30. A bucket of height 12 cm, has a top and bottom diameter of 40 cm and 20 cm respectively. The cost of tin sheet used for making the bucket at the rate of Rs. 1.20 per dm2 will be
Rs. 21.44
Rs  45.50
Rs. 60.45
Rs. 20.67
Q31. A hemisphere of lead of radius 9 cm is cast into a right circular cone of height 72 cm. The radius of the base of cone is
3 cm
5.4 cm
6 cm
4.5 cm
Q32. The volume of a sphere (in cu. cm) is equal to its surface area (in sq. cm). The diameter of the sphere (in cm) is
3
6
2
4
Q33. The radii of two cylinders are in the ratio 2:3. If their heights are in the ratio 3:5, then the ratio of their curved surface areas is 
3:5
2:5
1:2
2:7
Q34. If the radii of circular ends of frustum of a cone are 20 cm and 12 cm and its height is 6 cm, then the slant height of frustum (in cm) is:
10
8
12
15
Q35. If a right angled triangle is revolved about one of the sides containing the right angle it forms a
Right triangle
Right circular cone
Prism
Pyramid
Q36. A right circular cylinder of radius r cm and height h cm (h>2r) just enclosed a sphere of diameter
r cm
2r cm
h cm
2h cm
Q37. A largest sphere is carved out of a cube of side 7 cm. The volume of the sphere is
179.67 cu.cm
180.5 cu.cm
182 cu.cm
176.42 cu.cm
Q38. The diameter of a sphere is 12 cm. It is melted and drawn into a wire of diameter 6 mm. The length of the wire is 
32 mm
3.2 cm
0.32 m
None of these
Q39. If the height of a right circular cylinder is doubled keeping the radius the same, then the ratio of the volume of the cylinder thus obtained to the volume of the original cylinder is 
1:2
1:3
2:1
1:4
Q40. How many coins 1.75 cm in diameter and 2 mm thick must be melted to form a cuboid 11 cm x 10 cm x 7 cm?
16
1600
160
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