IUC AcademyHome1. The ratio of volume of two spheres is 64:125. What is the ratio of their surface areas?
- A. 4/25
- B. 4/5
- C. 16/25
- D. 25/16
Answer: 16/25
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2. A sphere is placed in a cube so that it touches all the faces of the cube. If 'a' is the ratio of t he volume of the cube to the volume of the sphere, and 'b' is the ratio of the surface area of the sphere to the surface area of the cube, then the value of ab is
- A. 1
- B. 36π2
- C. 4
- D. 236π
Answer: 1
3. A cylindrical vessel with radius 6 cm and height 5 cm is to be made by melting a number of spherical metal balls of diameter 2 cm. The minimum number of balls needed is
- A. 125
- B. 115
- C. 135
- D. 105
Answer: 135
Explanation: 2r 2cm r 1cm= =Q , Volume of spherical ball = 34 r3 π = 43 π Volume of cylindrical vessel = 2r hπ (Qr = 6cm, h = 5cm) = 180 π Required number of sphere = 1804 3 π π = 180 × 34 = 135 Hence, The minimum number of balls needed is 135.
Explanation: 2r 2cm r 1cm= =Q , Volume of spherical ball = 34 r3 π = 43 π Volume of cylindrical vessel = 2r hπ (Qr = 6cm, h = 5cm) = 180 π Required number of sphere = 1804 3 π π = 180 × 34 = 135 Hence, The minimum number of balls needed is 135.
4. A right circular cone of largest volume is cut out from a solid wooden hemisphere. The remaining material is what percentage of the volume of the original hemisphere?
- A. 75%
- B. 33½%
- C. 50%
- D. 66⅔%
Answer: 50%
5. A solid metallic sphere of radius x cm is melted and then drawn into 126 cones each of radius 3.5 cm and height 3 cm. There is no wastage of material in this process. What is the value of x?
- A. 3.5
- B. 7
- C. 10.5
- D. 21
Answer: 10.5
6. A solid lead sphere of radius 11 cm is melted and recast into small solid spheres of radius 2 cm each. How many maximum number (in integer) of such spheres can be made?
- A. 100
- B. 125
- C. 166
- D. 30
Answer: 166
7. The ratio of the total surface area and volume of a sphere is 2:7. Its radius is
- A. 10 cm
- B. 7.5 cm
- C. 10.5 cm
- D. 7 cm
Answer: 10.5 cm
Explanation: Total surface area of sphereVolume of shphere = 27 2 3 4 R 2 4 7R3 π⇒ = π 3 2R 7⇒ = R 10.5⇒ = cm
Explanation: Total surface area of sphereVolume of shphere = 27 2 3 4 R 2 4 7R3 π⇒ = π 3 2R 7⇒ = R 10.5⇒ = cm
8. If the surface area of two spheres is in the ratio of 49 : 25, then the ratio of their volumes will be
- A. 64 : 27
- B. 25 : 49
- C. 343 : 64
- D. 343 : 125
Answer: 343 : 125
9. The internal and external radii of a hollow hemispherical vessel are 6 cm and 7 cm respectively. What is the total surface area (in cm2) of the vessel ?
- A. 183 π
- B. 177 π
- C. 189 π
- D. 174 π
Answer: 183 π
10. A hemispherical bowl of internal diameter 36 cm is full of a liquid. This liquid is to be filled into cylindrical bottles each of radius 3 cm and height 12 cm. How many such bottles are required to empty the bowl ?
- A. 54
- B. 36
- C. 72
- D. 27
Answer: 36
11. A sphere of maximum volume is cut out from a solid hemisphere. What is the ratio of the volume of the sphere to that of the remaining solid ?
- A. 1 : 4
- B. 1 : 3
- C. 1 : 1
- D. 1 : 2
Answer: 1 : 3
12. The internal diameter of a hollow hemispherical vessel is 24 cm. It is made of a steel sheet which is 0.5 cm thick. What is the total surface area (in cm 2) of the vessel ?
- A. 468.75 π
- B. 600.5 π
- C. 600.2 π
- D. 612.75 π
Answer: 612.75 π
13. A hollow sphere is melted to form small identical hollow spheres. Inner and outer radius of the bigger sphere are 4 cm and 6 cm respectively. If inner and outer radii of the smaller sphere are 2 cm and 3 cm respectively, then how many smaller spheres can be formed?
- A. 4
- B. 8
- C. 6
- D. 12
Answer: 8
14. A prism and a pyramid have the same base and the same height. Find the ratio of volumes of prism and pyramid.
- A. 3:1
- B. 1:3
- C. 2:3
- D. 3:2
Answer: 3:1
Explanation: Volume of prism : Volume of Pyramid = (Area of base × Height) : 13 × Area of bases × Height = 3 : 1
Explanation: Volume of prism : Volume of Pyramid = (Area of base × Height) : 13 × Area of bases × Height = 3 : 1
15. A sphere of radius 4 cm is melted and recast into smallest spheres of radii 2 cm each. How many such spheres can be made?
- A. 8
- B. 4
- C. 16
- D. 32
Answer: 8
16. The number of lead balls, each 3 cm in diameter, that can be made from a solid lead sphere of diameter 42 cm is
- A. 2742
- B. 2744
- C. 7244
- D. 4722
Answer: 2744
17. A solid metallic sphere of radius 12 cm is melted and recast in the form of small spheres of radius 2 cm. How many small spheres are formed?
- A. 864
- B. 96
- C. 216
- D. 24
Answer: 216
18. A solid metallic hemisphere of radius 6.3 cm is melted and recast into a right circular cylinder of radius 9 cm. What is the height (in cm, correct to one decimal place) of the cylinder?
- A. 1.9
- B. 2.7
- C. 2.5
- D. 2.1
Answer: 2.1
19. A solid metallic sphere of radius 10 cm is melted and recast into spheres of radius 2 cm each. How many such spheres can be made?
- A. 64
- B. 216
- C. 100
- D. 125
Answer: 125
20. What is the volume (in cm 3) of a spherical shell whose inner and outer radii are respectively 2 cm and 3 cm ?
- A. 863π
- B. 563π
- C. 1063 π
- D. 763π
Answer: 763π
21. What is the total surface area of a pyramid whose base is a square of side 8cm and height of the pyramid is 3 cm?
- A. 169 cm2
- B. 121 cm2
- C. 184 cm2
- D. 144 cm2
Answer: 144 cm2
22. The radius of a sphere is 9 cm. It is melted and drawn into a wire of radius 0.3 cm. The length of the wire is
- A. 112 m
- B. 108 m
- C. 118 m
- D. 106 m
Answer: 108 m
23. If the surface area of a sphere is 1386 cm 2, then radius of the sphere.
- A. 12.5 cm
- B. 10 cm
- C. 10.5 cm
- D. 12 cm
Answer: 10.5 cm
24. How many maximum litres of milk can a hemispherical bowl of diameter 9 cm hold approximately ?
- A. 0.90 L
- B. 0.0191 L
- C. 1.90 L
- D. 0.191 L
Answer: 0.191 L
25. The internal and external diameters of a hollow hemispherical bowl are 6 cm and 10 cm respectively. If it is melted and cast into a solid cylinder of diameter 14 cm, what will be the height of the cylinder in cm?
- A. 1
- B. 1.33
- C. 1.22
- D. 1.1
Answer: 1.33
26. If the volume of a sphere is 4851 cm 3 then what is its diameter (in cm)?
- A. 21
- B. 16
- C. 18
- D. 12
Answer: 21
27. The volume of a solid hemisphere is 1904 cm 3. What will be its total surface area (in cm 2)?
- A. 2079
- B. 4158
- C. 3465
- D. 2772
Answer: 4158
Explanation: Volume of Hemisphere = 19404 cm 32 r 194043 π = 3 19404 3 7r 2 22× ×= × r3 = 9261 r = 21 cm Total surface area of hemisphere = 3 πr2 223 21 217= × × × = 4158 cm2
Explanation: Volume of Hemisphere = 19404 cm 32 r 194043 π = 3 19404 3 7r 2 22× ×= × r3 = 9261 r = 21 cm Total surface area of hemisphere = 3 πr2 223 21 217= × × × = 4158 cm2
28. The radius of a hemisphere is 6.3 cm what will be its volume?
- A. 523.90 cm3
- B. 572.80 cm3
- C. 643.50 cm3
- D. 353.38 cm3
Answer: 523.90 cm3
29. If the diameter of a sphere is 3.5 cm, then What is the total surface area of the sphere?
- A. 34.25 cm2
- B. 38. 5 cm2
- C. 45.75 cm2
- D. 42.6 cm2
Answer: 38. 5 cm2
30. If the diameter of a sphere is 63 cm then, what is the total surface area of the sphere?
- A. 11248 cm2
- B. 11824 cm2
- C. 12836 cm2
- D. 12474 cm2
Answer: 12474 cm2
31. If the diameter of hemisphere is 28 cm, then what is the volume of hemisphere?
- A. 6349.22 cm 3
- B. 6728.11 cm 3
- C. 5124.44 cm 3
- D. 5749.33 cm 3
Answer: 5749.33 cm 3
32. A hemispherical of lead of radius 4 cm is ca st into a right circular cone of height 72 cm. What is the radius of the base of the cone?
- A. 1.33 cm
- B. 1.63 cm
- C. 1.45 cm
- D. 1.35 cm
Answer: 1.33 cm
Explanation: Volume of Hemisphere = Volume of Cone 3 22 1R r h3 3π = π 2 × 4 × 4 × 4 = r2 × 72 r 2 = 169 r = 4 1.33cm3 = Hence, the radius of the base of the cone is 1.33 c m.
Explanation: Volume of Hemisphere = Volume of Cone 3 22 1R r h3 3π = π 2 × 4 × 4 × 4 = r2 × 72 r 2 = 169 r = 4 1.33cm3 = Hence, the radius of the base of the cone is 1.33 c m.
33. The curved surface area of a sphere is 154 cm 2. Find the volume of the sphere (rounded off to one digit after decimal).
- A. 161.1 cm3
- B. 147.8 cm3
- C. 156.9 cm3
- D. 179.7 cm3
Answer: 179.7 cm3
34. The radius of a hemisphere is 5.6 cm. What will be its volume?
- A. 265.65 cm3
- B. 380 cm3
- C. 367.95 cm3
- D. 195.95 cm3
Answer: 367.95 cm3
35. If the volume of a sphere is 38808 cm 3 then its surface area is
- A. 4433cm2
- B. 4455cm2
- C. 5544cm2
- D. 3344cm2
Answer: 5544cm2
36. A hemispherical bowl of radius 30 cm is filled with water by using a cylindrical glass. If the water from the cylindrical glass is poured 72 times to fill the bowl completely and the height of the glass is 10 cm. Then what is the base radius of the cylindrical glass.
- A. 8 cm
- B. 7.5 cm
- C. 5 cm
- D. 6 cm
Answer: 5 cm
37. How many spherical balls of 10 cm diameter can be made from a cylinder of height 35 cm and base radius 10 cm?
- A. 21
- B. 15
- C. 42
- D. 60
Answer: 21
38. What is the total surface area of solid hemisphere of diameter 14 cm?
- A. 584cm2
- B. 428cm2
- C. 522cm2
- D. 462cm2
Answer: 462cm2
39. A hemisphere of radius 7 cm is melted and made into four small identical spheres . Find the radius of these spheres?
- A. 3 cm
- B. 4 cm
- C. 3.5 cm
- D. 4.5 cm
Answer: 3.5 cm
40. Find the volume of the largest possible sphere circumscribed by a cube of edge 7 cm.
- A. 179.67 cm3
- B. 169.67 cm3
- C. 199.67 cm3
- D. 189.67 cm3
Answer: 179.67 cm3
41. A hemispherical bowl is made of 1 cm thick steel. The inner radius of the bowl is 4 cm. What the volume (cm 3) of steel used in making the bowl?
- A. 240 π 3
- B. 135 π 3
- C. 127 π 3
- D. 141 π 3
Answer: 240 π 3
Explanation: Width of Bowl (d) = 1 cm Inner radius (r) = 4cm Outer radius (R) = r + d = 4 + 1 = 5 cm Therefore, the volume of steel used in the hemisphe rical bowl = 23 π (R3 - r3) = 23 π (53 - 43) = 3122 2 40 cm3 3π = π Therefore the volume of the steel used to make the hemi bowl = 240 3 π cm3.
Explanation: Width of Bowl (d) = 1 cm Inner radius (r) = 4cm Outer radius (R) = r + d = 4 + 1 = 5 cm Therefore, the volume of steel used in the hemisphe rical bowl = 23 π (R3 - r3) = 23 π (53 - 43) = 3122 2 40 cm3 3π = π Therefore the volume of the steel used to make the hemi bowl = 240 3 π cm3.
42. The diameter of a metal sphere is 6 cm. By melting it, a wire is made, the diameter of whose cross section is 0.4 cm. Find the length of the wire (in meters).
- A. 12
- B. 18
- C. 9
- D. 10
Answer: 9
43. Height of a right circular cone is 8 cm. If diameter of its base is 12 cm, then what will be the curved surface area of the cone?
- A. 1056/7 cm 2
- B. 1320/7 cm 2
- C. 1440/7 cm 2
- D. 2112/7 cm 2
Answer: 1320/7 cm 2
44. The volume of a perpendicular cone is equal to the volume of that perpendicular cylinder whose height is 27 cm and diameter of its base is 30 cm. If the height of the cone is 25 cm, then what will be the diameter of its base?
- A. 24 cm
- B. 54 cm
- C. 27 cm
- D. 35 cm
Answer: 54 cm
45. The volume of a circular cone is equal to the sphere whose radius is half of the radius of the base of the cone. What is the ratio of the radius of the base of the cone to its height ?
- A. 1 : 4
- B. 4 : 1
- C. 1 : 2
- D. 2 : 1
Answer: 2 : 1
46. A conical vessel whose internal base radius is 18cm and height 60cm is full of a liquid. The entire liquid of the vessel is emptied into a cylindrical vessel with internal radius 15cm. The height (in cm) to which the liquid rises in the cylindrical vessel is?
- A. 24cm
- B. 30.2cm
- C. 27cm
- D. 28.8cm
Answer: 28.8cm
47. If the radius of the base of a cone is doubled , and the volume of the new cone is three times the volume of the original cone, then what will be the ratio of the height of the original cone to that of the new cone ?
- A. 9 : 4
- B. 4 : 3
- C. 2 : 9
- D. 1 : 3
Answer: 4 : 3
48. Radius of base of a hollow cone is 8 cm and it s height is 15 cm. A sphere of largest radius is put inside the cone. What is the ratio of radius of base of cone to the radius of sphere?
- A. 5 : 3
- B. 4 : 1
- C. 2 : 1
- D. 7 : 3
Answer: 5 : 3
Explanation: Let OD = OE = r cm Radiuses ∴ 2 2 2AC AD DC= + 2 2AC 15 8= + = 17cm ∴ ∆AEO ~ ∆ADC EO AODC AC= 15 rr8 17 -= 17r = 120 - 8r 120 24r 25 5= = Required ratio 248 :5= = 5 : 3
Explanation: Let OD = OE = r cm Radiuses ∴ 2 2 2AC AD DC= + 2 2AC 15 8= + = 17cm ∴ ∆AEO ~ ∆ADC EO AODC AC= 15 rr8 17 -= 17r = 120 - 8r 120 24r 25 5= = Required ratio 248 :5= = 5 : 3
49. A cone of radius 90 cm and height 120 cm stands on its base. It is cut into 3 parts by 2 cuts parallel to its base such that the height of the three parts (from top to bottom) are in ratio of 1 : 2 : 3. What is the total surface area (in cm2) of the middle part ?
- A. 14600
- B. 16500
- C. 17800
- D. 18500
Answer: 16500
50. Four identical cones each of radius 10.5 cm an d height 14 cm are cut from a cuboid of dimensions 30 cm × 32 cm × 40 cm (base of each cone lies on the surface of cuboid). What is the total surface area (in cm 2) of the remaining solid?
- A. 6528
- B. 7804
- C. 5926
- D. 6824
Answer: 7804
51. The height of a cone is 45 cm. It is cut at a height of 15 cm from its base by a plane parallel to its base. If the volume of the smaller cone is 18480 cm 3, then what is the volume (in cm3) of the original cone?
- A. 34650
- B. 61600
- C. 36960
- D. 62370
Answer: 62370
52. The height of the cylindrical bucket is 27cm and base radius is 48cm and the bucket is filled with sand. When the bucket is emptied then a pile of cone of 54 cm radius is formed. What is the height of the pile (in cm)?
- A. 32
- B. 56
- C. 54
- D. 64
Answer: 64
53. The volume of a right circular cone is 462 cm 3. If its height is 12 cm, then the area of its base (in cm2) is
- A. 103.5
- B. 115.5
- C. 98.5
- D. 124.5
Answer: 115.5
Explanation: Volume of right circular cone = 1 area of base height3 × × 462 = 1 area of base 123 × × Area of base = 462 312× = 115.5 cm2
Explanation: Volume of right circular cone = 1 area of base height3 × × 462 = 1 area of base 123 × × Area of base = 462 312× = 115.5 cm2
54. A container in the shape of a right circular cone, whose radius and depth are equal, gets completely filled by 128000 spherical droplets, each of diameter 2 mm. What is the radius (in cm) of the container?
- A. 6
- B. 4
- C. 8
- D. 2
Answer: 8
55. The ratio of heights of two cones is 2 : 1 and the ratio of their radii is 1: 2. Find the ratio of the ir volumes.
- A. 4 : 3
- B. 2 : 1
- C. 1 : 2
- D. 3 : 4
Answer: 1 : 2
56. The radius of a solid right circular cone is 36 cm and its height is 105 cm. What will be the total surface area (cm2) of the cone?
- A. 5292 π
- B. 4296 π
- C. 3969 π
- D. 3996 π
Answer: 5292 π
57. The volume of a cone, whose base radius and height are r and h respectively , is 400 cm 3 . What will be the volume of a cone, whose base radius and height are 2r cm and h cm respectively ?
- A. 1200 cm3
- B. 100 cm3
- C. 800 cm3
- D. 1600 cm3
Answer: 1600 cm3
58. The area of the base of a solid cone is 616cm 2. If the height of the cone is 15 cm, then what is the volume of this cone?
- A. 3440 cm3
- B. 2940 cm3
- C. 3190 cm3
- D. 3080 cm3
Answer: 3080 cm3
Explanation: Area of base of cone = 616 cm 2 Height of cone = 15 cm Volume of cone 13= × base of area × height 1 616 153= × × = 3080 cm3
Explanation: Area of base of cone = 616 cm 2 Height of cone = 15 cm Volume of cone 13= × base of area × height 1 616 153= × × = 3080 cm3
59. What will be the total surface area of a cone of base radius 6 cm and height 8 cm?
- A. 301.71 cm2
- B. 350.51 cm2
- C. 364.61 cm2
- D. 354.50 cm2
Answer: 301.71 cm2
Explanation: Given that, r = 6cm h = 8cm Slant height (l) 2 2 2 2(r) (h) (6) (8) 10cm= + = + = Total surface area of cone = πr(l + r) 22 6(10 6)7= × + 22 6 167= × × = 301.71 cm 2
Explanation: Given that, r = 6cm h = 8cm Slant height (l) 2 2 2 2(r) (h) (6) (8) 10cm= + = + = Total surface area of cone = πr(l + r) 22 6(10 6)7= × + 22 6 167= × × = 301.71 cm 2
60. A conical tent of radius 6 units and height 8 units is to be made by a canvas. How much canvas is needed to make the tent? (rounded off to given decimal place).
- A. 177.55 square unit
- B. 166.57 square unit
- C. 188.57 square unit
- D. 155.87 square unit
Answer: 188.57 square unit
Explanation: Given that, Radius (r) = 6 unit height (h) = 8 unit Slant height (l) 2 2(8) (6)= + 64 36= + = 10 unit ง Canvas is required to make the tent = πrl 22 6 107= × × 13207= = 188.57 unit 2
Explanation: Given that, Radius (r) = 6 unit height (h) = 8 unit Slant height (l) 2 2(8) (6)= + 64 36= + = 10 unit ง Canvas is required to make the tent = πrl 22 6 107= × × 13207= = 188.57 unit 2
61. The height of a right circular cone is 20 and the diameter of its base is 30. What is the curved surface area and total surface area of the right circular cone respectively?
- A. 450 π cm2 and 625π cm2
- B. 390 π cm2 and 475π cm2
- C. 335 π cm2 and 525π cm2
- D. 375 π cm2 and 600π cm2
Answer: 375 π cm2 and 600π cm2
62. The volume of a right circular cylinder is 3 times the volume of a right circular cone. The radius of the cone and the cylinder are 3cm and 6 cm respectively. If the height of the cylinder is 1 cm, then what is the slant height of the cone?
- A. 13cm
- B. 4 cm
- C. 5 cm
- D. 6 cm
Answer: 5 cm
Explanation: According to the question Volume of cylinder = volume of cone × 3 π r2h= 21 R H 33 × π × 2 2r h R H= (6) 2 ×1 = (3)2 ×H 36 = 9 × H H = 4cm ∴ The slant height of cone 2 2 2 2H R (4) (3)= + = + 16 9 25= + = = 5cm
Explanation: According to the question Volume of cylinder = volume of cone × 3 π r2h= 21 R H 33 × π × 2 2r h R H= (6) 2 ×1 = (3)2 ×H 36 = 9 × H H = 4cm ∴ The slant height of cone 2 2 2 2H R (4) (3)= + = + 16 9 25= + = = 5cm
63. The radii of two cylinders A and B are in the ratio of 5 : 6 and the heights are in the ratio of 7 : 4 respectively. The ratio of curved surface area of cylinder B to that of A is
- A. 35 : 24
- B. 24 : 35
- C. 49 : 35
- D. 35 : 49
Answer: 24 : 35
64. The diameter of a right circular cylinder is decreased to one third of its initial value. If the volume of the cylinder remains the same, then the height becomes how many times of the initial height.
- A. 1
- B. 9
- C. 6
- D. 3
Answer: 9
65. The length and the breadth of rectangle are 15 cm and 12cm respectively. If the rectangle is given on full rotation about its breadth as the axis. What is the volume (in cm 3) through which the rectangle moves?
- A. 2160 π
- B. 1440 π
- C. 1800 π
- D. 2700 π
Answer: 2700 π
66. The curved surface area of cylinder is 25344 cm2 and its height is 32 cm. What is the volume of cylinder whose capacity is π792 times the volume of the cylinder?
- A. 3168 cm3
- B. 6336 cm3
- C. 1584 cm3
- D. 9504 cm3
Answer: 6336 cm3
67. If 3.96 cubic dm of lead is to be drawn into a cylindrical wire of diameter 0.6 cm, then the length of the wire (in metres), is
- A. 140 m
- B. 120 m
- C. 130 m
- D. 125 m
Answer: 140 m
68. Water flows into a tank 180 m × 140 m through a rectangular pipe of 1.2m × 0.75 m at a rate of 5 km/h. In what time will the water rise by 4 m?
- A. 6 hours 42 minutes
- B. 5 hours 46 minutes
- C. 7 hours 28 minutes
- D. 8 hours 12 minutes
Answer: 7 hours 28 minutes
69. The radius of base of a cylinder is 7cm and its curved surface area is 440cm2. Its volume will be
- A. 1760
- B. 1540
- C. 1430
- D. 1650
Answer: 1540
70. A rectangular sheet of paper which is 88cm long and 11cm wide is rolled to form a cylinder of height equal to its width of the paper. What is the volume of the cylinder so formed?"
- A. 7676 cm 3
- B. 6786 cm 3
- C. 6776 cm 3
- D. 6546 cm 3
Answer: 6776 cm 3
Explanation: Height of cylinder after folding the paper (h) = 11 cm Perimeter of cylinder = 88 cm 2 π r = 88 r = 14 cm Volume of cylinder = 2 22r h 14 14 117π = × × × = 6776 cm 3
Explanation: Height of cylinder after folding the paper (h) = 11 cm Perimeter of cylinder = 88 cm 2 π r = 88 r = 14 cm Volume of cylinder = 2 22r h 14 14 117π = × × × = 6776 cm 3
71. Let A and B be two cylinders such that the capacity of A is the same as the capacity of B. The ratio of the diameters of A and B is 1:4. What is the ratio of the heights of A and B?
- A. 16:1
- B. 1:16
- C. 3:16
- D. 16:3
Answer: 16:1
72. The base of a right prism is a triangle with sides 16cm, 30 cm and 34 cm. Its height is 32 cm. The lateral surface area (in cm 2) and the volumes (in cm3) are respectively.
- A. 2688 and 7680
- B. 2560 and 6400
- C. 2624 and 7040
- D. 2560 and 7680
Answer: 2560 and 7680
Explanation: Sides of triangle are 16, 30 and 34 cm. From Pythagoras theorem, (Hypotenuse)2 = (Perpendicular)2 + (Base)2 (34)2 = (16)2 + (30)2 1156 = 256 + 900 1156 = 1156 So, triangle is right angle triangle Volume of prism = Base area × Height 1 b h2= × × × l 1 16 30 322= × × × = 7680 cm3 Lateral surface area of a prism = Base perimeter × Height = (16 + 30 + 34) × 32 = 80 × 32 = 2560 cm2
Explanation: Sides of triangle are 16, 30 and 34 cm. From Pythagoras theorem, (Hypotenuse)2 = (Perpendicular)2 + (Base)2 (34)2 = (16)2 + (30)2 1156 = 256 + 900 1156 = 1156 So, triangle is right angle triangle Volume of prism = Base area × Height 1 b h2= × × × l 1 16 30 322= × × × = 7680 cm3 Lateral surface area of a prism = Base perimeter × Height = (16 + 30 + 34) × 32 = 80 × 32 = 2560 cm2
73. A hollow cylinder of thickness 0.7 cm and height 15 cm is made of iron. If inner radius of cylinder is 3.5 cm, then what is the total surface area (in cm2) of the hollow cylinder ?
- A. 812.12
- B. 768.42
- C. 759.88
- D. 828.42
Answer: 759.88
74. A hollow cylinder is made up of metal. The difference between outer and inner curved surface area of this cylinder is 352 cm 2. Height of the cylinder is 28 cm. If the total surface area of this hollow cylinder is 2640 cm 2, then what are the inner and outer radius (in cm) ?
- A. 4, 6
- B. 10, 12
- C. 8, 10
- D. 6, 8
Answer: 6, 8
75. The curved surface area of a cylinder is 594 cm2 and its volume is 1336.5 cm 3. What is the height (in cm) of the cylinder ?
- A. 14
- B. 21
- C. 24.5
- D. 10.5
Answer: 21
76. The radius of base of a solid cylinder is 7 cm and its height is 21 cm. It is melted and converted into small bullets. Each bullet is of same size. Each bullet consisted of two parts viz. a cylinder and a hemisphere on one of its base. The total height of bullet is 3.5 cm and radius of base is 2.1 cm. Approximately how many complete bullets can be obtained?
- A. 83
- B. 89
- C. 74
- D. 79
Answer: 83
Explanation: Let, Total number of bullets = n Height of cylindrical bullets (h) = 3.5 - 2.1 = 1.4 cm Total volume of solid cylinder = Number of total bullets × Volume of small bullets 2 2R H n 2.1 2.1 1.4 . 2.1 2.1 2.13[ ]π× = × π× × × + π× × × [ ]7 7 21 n 2.1 2.1 1.4 1.4× × = × × + 7 7 21h 2.1 2.1 2.8× ×= × × = 83.33 83≈
Explanation: Let, Total number of bullets = n Height of cylindrical bullets (h) = 3.5 - 2.1 = 1.4 cm Total volume of solid cylinder = Number of total bullets × Volume of small bullets 2 2R H n 2.1 2.1 1.4 . 2.1 2.1 2.13[ ]π× = × π× × × + π× × × [ ]7 7 21 n 2.1 2.1 1.4 1.4× × = × × + 7 7 21h 2.1 2.1 2.8× ×= × × = 83.33 83≈
77. The ratio of curved surface area of a right circular cylinder to the total area of its two bases is 2 : 1. If the total surface area of cylinder is 23100 cm 2, then what is the volume (in cm3) of cylinder?
- A. 247200
- B. 269500
- C. 312500
- D. 341800
Answer: 269500
Explanation: According to the question Area of curved surface of cylinder = 2 × Sum of area of base 22 rh 2 2 rπ = × π h = 2r Total surface area of cylinder 2 r(h r)= π + 23100 = 22 r(2r r) 6 r= π + = π r = 35 cm Volume of cylinder 2 3r h 2 r= π = π 222 35 35 357= × = 269500 cm3
Explanation: According to the question Area of curved surface of cylinder = 2 × Sum of area of base 22 rh 2 2 rπ = × π h = 2r Total surface area of cylinder 2 r(h r)= π + 23100 = 22 r(2r r) 6 r= π + = π r = 35 cm Volume of cylinder 2 3r h 2 r= π = π 222 35 35 357= × = 269500 cm3
78. The lateral surface area of a cylinder is 352 cm2. If its height is 7 cm, then its volume (in cm3) is : (Take 22π =7 )
- A. 1243
- B. 891
- C. 1078
- D. 1408
Answer: 1408
79. If the radius of a right circular cylinder is decreased by 20% while its height is increased by 40%, then the percentage change in its volume will be
- A. 10.4% decrease
- B. 1.04% increase
- C. No increase or decrease
- D. 10.4% Increase
Answer: 10.4% decrease
80. The ratio of the volumes of two cylinders is x : y and the ratio of their diameters is a : b. What is the ratio of their heights ?
- A. xb : ya
- B. xb 2 : ya2
- C. xa : yb
- D. xa 2 : yb2
Answer: xb 2 : ya2