Total Time: 90 mins Practise Exercise no. 1 Total no. Of Qs: 51

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1 Mensuration (3-D) Total Time: 90 mins Practise Exercise no. 1 Total no. Of Qs: 51 Q1. A wooden box of dimensions 8m x 7m x 6m is to carry rectangular boxes of dimensions 8cm x 7cm x 6cm. The maximum number of boxes that can be carried in the wooden box is: a) b) c) d) Q2. A tank 3 m long, 2 m wide and 1.5 m deep is dug in a field 22 m long and 14 m wide. If the earth dug out is evenly spread out over the field, the level of the field will rise by nearly: Q6. If the length, breadth and height of a rectangular parallelepiped are in the ratio 6:5:4 and if total surface area is 33,300m 2 then the length breadth and height of a parallelepiped (in cm) respectively are: a) 90, 85, 60 b) 90, 75, 70 c) 85, 75, 60 d) 90, 75, 60 Q7.The sum of length, breadth and height of a cuboid is 26 cm and its diagonal is 14 cm long. Find the total surface are of cuboid. a)0.299 cm b) 0.29mm a) 840 sq cm b) 480 sq cm c) 2.98 mm d) 4.45cm Q3. A river 10 metres deep and 200 metres wide is flowing at the rate of 4 1\2 km/hr. Find how many cubic m of water run into the sea per second. a) 2500 cub metres b) 2000 cub metres c) 2200 cub metres d) None of these Q4. The area of a side of a box is 120 sq cm. The area of the other side of the box is 72 sq cm. If the area of the upper surface of the box is 60 sq cm then find the volume of the box. a) cm 3 b) cm 3 c) 720 cm 3 d) Can t be determined Q5. If the length, breadth and height of a cuboid are 2m, 2m, 1m respectively then its surface area (in m 2) is: a) 8 b) 12 c) 450 sq cm d) None of these Q8. A cubic metre of copper weighing 9000 kilograms is rolled into a square bar 9 metres long. An exact cube is cut off from the bar. How much does it weigh? a) 333 1/3kg b) 233 1/3 kg c) 334 1/3 d) 333 1/2 kg Q9. A hollow garden roller 63 cm wide with a girth of 440 cm is made of iron 4 cm thick. The volume of iron is: a) cm 3 b) cm 3 c) 54982cm 3 d) 57636cm 3 Q10. The radius of wire is decreased to one third. If volume remains same, length will increase: a) 1 time b) 6 times c) 3 times d) 9 times c) 16 d) 24 Page 1

2 Q11. If the diameter of the base of a closed right circular cylinder is equal to its height h, then its whole surface area is: a) 2h 2 b) 4/3 h 2 c) 3/2 h 2 d) h 2 Q12. A metal sphere of diameter 42 cm is dropped into a cylindrical vessel, which is partly filled with water. The diameter of the vessel is 1.68 metres. If the sphere is completely submerged, find by how much the surface of water will rise. a) 1.75 b) 2.75 c) 2 cm d) 1 cm Q13. The number of solid spheres of radius 1/4 cm, which may be formed from a solid sphere of radius 4 cm, is: a) 4096 b) 4964 c) 6904 d) 9640 Q14. If a solid sphere of radius 10 cm is moduled into 8 spherical solid balls of equal radius, then surface area of each ball (in cm 2 ), is: a) 100 b) 75 c) 60 d) 50 Q15. If the volumes of surface area of a sphere are numerically the same, then its radius is: a) 1 unit b) 2 units c) 3 units d) 4 units Q16. A hemispherical bowl has inner diameter 42 cm. The quantity of liquid that the bowl can hold in cm 3 ) is: a) 2/3 (21) 3 b) 2/3 7/22 (21) 3 c) 3/2 22/7 (21) 3 d) 2/3 7/22 (42) 3 Q17. If a right circular cone of vertical height 24 cm has a volume of 1232 cm 3, then the area of its curved surface in cm 2 is: a) 1254 b) 704 c) 550 d) 154 Q18. A right cylindrical vessel is full with water. How many right cones having same diameter and height as those of right cylinder will be needed to store that water? a) 2 b) 3 c) 4 d) 5 Q19. A cylindrical piece of metal of radius 2 cm and height 6 cm is shaped into a cone of same radius. The height of the cone is? a) 18 cm b) 14 cm c) 12 cm d) 8 cm Q20. A Reservoir is in the shape of a frustum of a right circular cone. It is 8 m across at the top and 4 m across the bottom. It is 6 m deep. Its capacity is: a) 176 m 3 b) 196m 3 c) 200m 3 d) 110 m 3 Q21. How many bricks 20cm X 10cm X 7.5cm a truck whose load is 5 Metric ton can carry? The bricks in question weigh 2500 kg per cubic meter a) 1333 b) 1233 c) 1332 d) 1433 Q22. In a shower 2cm of rain falls. Find in cubic meters the volume of water that falls on 6 hectare of ground? Page 2

3 a) Cub m b) 1200 cub m c) 1600 cub m d) Cannot be determined. Q23. A cubic metre of copper weighing 640 kilograms is rolled into a square bar16 metres long. An exact cube is cut off from the bar. How much does it weigh? a) 15 kg b) 32 kg c) 16 kg d) 10 kg Q24. The internal diameter of an iron pipe is 6 cm and the length is 2.8 metres. If the thickness of the metal be 5 mm and 1 cu cm of iron weighs 8 gm, find the weight of the pipe. a) kg b) 22.88kg c) kg d) None of these Q25. Find the volume of the material in a cylindrical tube in cubic dm, the radius of the outer surface being 10 dm the thickness 0.4 dm, and height 9 dm. a) cub m b) cub m c) cub m d) cub m Q26. A rectangular sheet with dimension 11 m x 8 m is rolled into a cylinder so that the smaller side becomes the height of the cylinder. What is the volume of the cylinder so formed? a) 77 cu m b) 87 cu m c) 87 cu m d) Data inadequate Q27. A copper sphere of diameter 18 cm is drawn into a wire of diameter 6 cm. Find the length of the wire? a) 108 cm b) 180 cm c) 190 cm d) Data inadequate Q28. A cylinder of radius 12 cm and height 20 cm is melted and the same mass is used to create a sphere. What will be the radius of the sphere? a) 12 cm b) 18 cm c) 15 cm d) Data inadequate Q29. A sphere is melted to form a cylinder whose height is 70 5/16 times its radius. What is the radii of sphere to the cylinder? a) 5:4 b) 11:4 c) 15:4 d) 13:4 Q30. There is a cone of radius 18 cm and height 24 cm. Find the radius of the greatest sphere that can be carved out of that cone? a) 9 cm b) 12 cm c) 6 cm d) Can t be determined Q31. The curved surface areas of two spheres are in the ratio1:2. Find the ratio of their volumes. a) 1: 2 b) 2:1 c) 2:2 2 d) 1:2 2 Q32. If the radii of two spheres are in the ratio 1:4, then ratio of their surface areas will be a) 1:2 b)1:4 c) 1:8 d) 1:16 Q33. Two circular cylinders of equal volume have their heights in ratio of 16:25. Ratio of their radii is? a) 4:5 b) 5:4 c) 3:2 d) 2:3 Q34. Two circular cylinders of equal volume have their heights in the ratio 16:25. Find the ratio of their curved surface areas. Page 3

4 a) 4:5 b) 5:4 c) 16:5 d) 4:25 Q35. If the volumes of the two cones are in the ratio 9:1 and their heights in the ratio 9:16, what is the ratio of their radii? a) 5:1 b)3:1 c) 4:1 d)4:3 Q36. If the heights and the curved surface areas of two circular cylinders are in the ratio 2:3 and 8:9 respectively. Find the ratio of their radii. a) 3:4 b) 4:3 c) 5:6 d) 16:9 Q37. 4 cm of rain has fallen on 2 square km of land. Assuming that 50%of the raindrops could have collected and contained in a pool having a 100m x 10 m base, by what level would the water level in the pool have increased? a) 40 m b) 60 m c) 80 m d) None of these Q38. A well with 14 meters inside diameter is dug 8 meters deep, Earth taken out of it has been evenly spread all around it to a width of 21 meters to form an embankment. The height of embankment is: a) 43 cm b) 47.6 cm c) 53.3 cm d) 41 cm Q39. A right- angled triangle having base 6 metres and height equal to 8 metres, is turned around the height. Find the volume of the cone thus formed. Also find the surface area. a) 96, 60 b) 48, 60 c) 96, 120 d) 48, 30 Q40. A right- angled triangle having base 6 metres and height equal to 8 metres, is turned around the base. Find the volume of the cone thus formed. Also find the surface area. a)128, 80 b) 182, 90 c) 128, 84 d) 128, 48 Q41. The length, breadth and height of a cuboid are made 2, 4 and 6 times respectively. Find the percentage increase in its volume. a) 4700% b) 47% c) 2300% d) 4800% Q42. The radius of a cylinder is increased by 45%. Keeping its height unchanged. What is the percentage increase in its volume? a) 82.5% b) 82.25% c) 70% d) 80.5% Q43. Each of the radius and the height of a right circular cylinder is both increased by 1%. Find the % by which the volume increases. a) 3% b) 3.03% c) 3.3% d) Data inadequate Q44. A right circular cone is exactly fitted inside a cube in such a way that the edges of the base of the cone are touching the edges of one of the faces of the cube and the vertex is on the opposite face of the cube. If the volume of the cube is 343cc, what approximately is the volume of the cone? a) 70cc b) 80cc c) 90cc d) 100cc Q45. Sum of the length, width and depth of a cuboid is s and its diagonal is d. Its surface area is: Page 4

5 a) S 2 b) d 2 c) s 2 -d 2 d) s 2 +d 2 a) Cube b) cone c) sphere d) cylinder Q46. A right cylinder and a right circular cone have same radius and same volume. The ratio of height of the cylinder of that of the cone is: a) 3:5 b) 2: 5 c) 3: 1 d) 1: 3 Q47. A right circular cone is cut off at the middle of its height and parallel to base. Call smaller cone thus formed A and remaining part B. Then: a)vola<volb b) Vol A = Vol B c)vola>vol B d) Vol A = Vol B/2 Q48. A solid consists of a circular cylinder with exact fitting right circular cone placed on the top. The height of the cone is h. If total volume of the solid is 3 times and volume of cone, then the height of circular cylinder is: a) 2h b) 4h c) 3h /2 d) 2h/3 Q49. The number of solid spheres, each of diameter 6 cm, that could be moulded to form a solid metal cylinder of height 45 cm and diameter 4 cm, is: a) 3 b) 4 c) 5 d) 6 Q50. The areas of two spheres are in the ratio I: 4. the ratio of their volumes is: a)1:4 b) 1 :2 2 c) 1:8 d) 1:64 Q51. For a given equal volume, which of the following has minimum surface area? Page 5

6 Mensuration 3-d practise exercise- 1 (Solutions) Q no. Answer Q no. Answer Q no. Answer 1 C 21 A 41 A 2 C 22 B 42 A 3 A 23 D 43 B 4 C 24 B 44 C 5 C 25 C 45 C 6 D 26 A 46 D 7 B 27 A 47 A 8 A 28 A 48 D 9 B 29 C 49 C 10 D 30 A 50 C 11 C 31 D 51 C 12 A 32 D 13 A 33 B 14 A 34 A 15 C 35 C 16 C 36 B 17 C 37 C 18 B 38 C 19 A 39 A 20 A 40 A

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