Volume and Surface Area Mathematic 1
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| Volume and Surface Area Mathematic 1 |
Important information:- Volume and surface area are related to solids or hollow bodies. These bodies occupy space and have usually three dimensions length, breadth and height.
#Volume:- Space occupied by an object is called the 'volume' of that particular object. It is always measured in cube unit like cubic meter, cubic centimeter etc.
#Surface Area:- Surface area of a solid body is the area of all of its surfaces together. Surface area is measured in square unit like square centimeter , square meter etc.
#Cube:- A solid body having 6 equal faces with equal length, breadth and height is called a cube. Infact, each face of a cube is a square.
#Cuboid:- A rectangular solid body having 6 rectangular faces is called a cuboid
#Room:- A rectangular room has 4 walls (surfaces) and opposite walls have equal areas.
#Box:- A box has its shape like cube or cuboid. The amount that a box can hold or contain, is called the capacity of the box. Infact , capacity is the internal volume
#Cylinder:- A cylinder is a solid or hollow body that is formed by keeping circles of equal radii one on another. Apart from this, a cylinder is formed by rolling a rectangular sheet also. A cylinder has three surfaces .
#Cone:- Cone is a solid or hollow body with a round base and pointed top. It is formed by the rotation of a triangle along any of the side
#Frustum:- of Cone If a cone is cut by a plane parallel to the base so as to divide the cone into two parts upper part and lower part, then the lower part is called frustum.
#Sphere:- A sphere is a three-dimensional solid figure, which is made up of all points in the space, which lie at a constant distance from a fixed point. That constant distance and fixed point are respectively called the radius and center of the sphere. In fact, a sphere is like a solid ball.
#Hollow Sphere or Spherical Shell:- Its both external and internal surfaces are spherical and both the surfaces have a common central point.
Table of Contain:-
Cone and Frustum of Cone
37. The curved surface area of a right circular cone of radius 14 cm is 440 sq cm. What is the slant height of the cone?
(a) 10 cm
(b) 11cm
(c) 12 cm
(d) 13 cm
Answer:- (a) 10 cm
38. The diameter of base of a right circular cone is 7 cm and slant height is 10 cm, then what is its lateral surface area ?
(a) 110 sq cm
(b) 100 sq cm
(c) 70 sq cm
(d) 49 sq cm
Answer:- (a) 110 sq cm
39. What is the whole surface area of a cone of base radius 7 cm and height 24 cm?
(a) 654 sq cm
(b) 704 sq cm
(c) 724 sq cm
(d) 964 sq cm
Answer:- (b) 704 sq cm
40. What is the volume of a cone having a base of radius 10 cm and height 21 cm?
(a) 2200 cm3
(b) 3000 cm3
(c) 5600 cm3
(d) 6600 cm3
Answer:- (a) 2200 cm3
41. The diameter of the base of a cone is 6 cm and altitude is 4 cm. What is the approximate curved surface area of the cone?
(a) 45 cm2
(b) 47 cm2
(c) 49 cm2
(d) 51 cm2
Answer:- (b) 47 cm2
42. The volume of a right circular cone is 100 n cm and its height is 12 cm. Find its slant height.
(a) 13 cm
(b) 16 cm
(c) 9 cm
(d) 26 cm
(e) None of the above
Answer:- (a) 13 cm
43. If the volume of a right circular cone of height 9 cm is 48 7t cm , then find the diameter of its base.
(a) 8 cm
(b) 4 cm
(c) 7 cm
(d) 11 cm
(e) None of the above
Answer:- (a) 8 cm
44. Shantanu's cap is in the form of a right circular cone of base radius 7 cm and height 24 cm. Find the area of the sheet required to make 5 such caps.
(a) 5000 sq cm
(b) 2750 sq cm
(c) 3000 sq cm
(d) 2700 sq cm
(e) None of the above
Answer:- (a) 5000 sq cm
45. The radius of the base of a right circular cone is doubled. To keep the volume fixed, the height of the cone will be?
(a) Half of the previous height
(b) One third of the previous height
(c) One fourth of the previous height
(d) 1/2 times of the previous height
Answer:- (c) One fourth of the previous height
46. The radius of the base of a right circular cone is increased by 15% keeping the height fixed.
The volume of the cone will be increased by ?
(a) 30%
(b) 31%
(c) 32.25%
(d) 34.75%
Answer:- (c) 32.25%
47. The frustum of a right circular cone has the diameters of base 10 cm, of top 6 cm and a height of 5 cm. Find its slant height.
(a) √ 29 cm
(b) 3√ 3 cm
(c) √ 13 cm
(d) 4√ 3 cm
(e) None of the above
Answer:- (a) √ 29 cm
48. The frustum of a right circular cone has the radii of base 4 cm, of the top 2 cm and a height of 6 cm. Find the volume of the frustum.
(a) 115 cm3
(b) 156 cm3
(c) 185 cm3
(d) 176 cm3
(e) None of the above
Answer:- (d) 176 cm3
49. A cone of radius r cm and height h cm is divided into two parts by drawing a plane through the middle point of its height and parallel to the base. What is the ratio of the volume of the original cone to the volume of the smaller cone?
(a) 4:1
(b) 8:1
(c) 2:1
(d) 6:1
Answer:- (b) 8:1
50. If the ratio of volumes of two cones is 2 : 3 and the ratio of the radii of their bases is 1 : 2, then the ratio of their heights will be
(a) 3 : 8
(b) 8 : 3
(c) 9 : 2
(d) 8 : 1
(e) None of the above
Answer:- (b) 8 : 3
51. The ratio of the radius and height of a 2 ^ cone is 5 : 12. Its volume is 314— cm . Its 7 slant height is ?
(a) 18 cm
(b) 13 cm
(c) 16 cm
(d) 15 cm
(e) None of the above
Answer:- (b) 13 cm
52. If the height of the right circular cone is increased by 200% and the radius of the base is reduced by 50%, then the volume of the cone ?
(a) increases by 25%
(b) increases by 50%
(c) remains unchanged
(d) decreases by 25%
(e) None of the above
Answer:- (d) decreases by 25%
53. If the volumes of two right circular cones are in the ratio 1 : 3 and their diameters are in the ratio 3 : 5, then the ratio of their heights is ?
(a) 25 : 27
(b) 1 : 5
(c) 3 : 5
(d) 5 : 27
Answer:- (a) 25 : 27
54. The diameters of two cones are equal. If their slant heights be in the ratio of 5 : 7, then find the ratio of their curved surface areas.
(a) 25 : 7
(b) 25 : 49
(c) 5 : 49
(d) 5 : 7
Answer:- (d) 5 : 7
55. A conical cap has the base diameter 24 cm and height 16 cm. What is the cost of painting the surface of the cap at the rate of 70 paise per sq cm?
(a) 520
(b) 524
(c) 528
(d) 532
Answer:- (c) 528
56. The curved surface area and the total surface area of a cylinder are in the ratio 1 : 2. If the total surface area of the right cylinder is 616 cm , then its volume is
(a) 1632 cm3
(b) 1078 cm3
(c) 1232 cm3
(d) 1848 cm3
Answer:- (b) 1078 cm3
Sphere
57. Weight of a solid metallic sphere of radius 4 cm is 4 kg. The weight of a hollow sphere made with same metal, whose outer diameter is 16 cm and inner diameter is 12 cm, is ?
(a) 20.5 kg
(b) 15.5 kg
(c) 16.5 kg
(d) 18.5 kg
Answer:- (d) 18.5 kg
58. If the radius of a sphere is increased by 100%, by what per cent does its volume increase?
(a) 300%
(b) 900%
(c) 500%
(d) 700%
(e) None of the above
Answer:- (d) 700%
59. If radius of a sphere is decreased by 24%, by what per cent does its surface area decrease?
(a) 44%
(b) 49%
(c) 42.24%
(d) 46.2%
(e) None of the above
Answer:- (c) 42.24%
60. What will be the surface area of the sphere having 4 cm radius?
(a) 64 sq cm
(b) 69 sq cm
(c) 32 sq cm
(d) 35 sq cm
Answer:- (a) 64 sq cm
61. What is the diameter of the largest circle lying on the surface of a sphere of surface area
616 sq cm?
(a) 14 cm
(b) 10.5 cm
(c) 7 cm
(d) 3.5 cm
Answer:- (a) 14 cm
62. The diameter of the Moon is approximately one-fourth of the diameter of the Earth. What is the ratio (approximate) of their volumes?
(a) 4:16
(b)1:64
(c)2:6
(d)1:128
Answer:- (b)1:64
63. If the radius of a sphere is increased by 3%, then what per cent increase takes place in surface area of the sphere?
(a) 6.09%
(b) 7%
(c) 5.06%
(d) 9%
(e) None of the above
Answer:- (a) 6.09%
64. A metallic sphere of radius 12 cm is melted into three smaller spheres. If the radii of two smaller spheres are 6 cm and 8 cm, the radius of the third is
(a) 14 cm
(b) 16 cm
(c) 10 cm
(d) 12 cm
Answer:- (c) 10 cm
65. Find the number of lead balls of diameter 2 cm each, that can be made from a sphere of diameter 16cm.
(a) 2048
(b) 512
(c) 2002
(d) 1520
(e) None of the above
Answer:- (b) 512
66. A hemispherical bowl has 3.5 cm radius. It is to be painted inside as well as outside. Find the cost of painting it at the rate of 5 per 10 sq cm.
(a) 50
(b) 81
(C) 56
(d) 77
(e) None of the above
Answer:- (d) 77
67. If the surface area of a sphere is 616 sq cm, what is its volume?
(a) 4312/3 cm3
(b) 4102/3 cm3
(c) 1257 cm3
(d) 1023 cm3
Answer:- (a) 4312/3 cm3
68. If the ratio of the diameters of two spheres is 3 : 5, then what is the ratio of their surface areas?
(a) 9 : 25
(b) 9 : 10
(c) 3 : 5
(d) 27 : 125
Answer:- (a) 9 : 25
69. If 64 identical small spheres are made out of a big sphere of diameter 8 cm, what is surface area of each small sphere?
(a) å…€ cm2
(b) 2å…€ cm2
(c) 4å…€cm2
(d) 8å…€ cm2
Answer:- (c) 4å…€cm2
70. A hemisphere has 28 cm diameter. Find its curved surface area.
(a) 1232 sq cm
(b) 1236 sq cm
(c) 1238 sq cm
(d) 1233 sq cm
Answer:- (a) 1232 sq cm
71. What will be the difference between total surface area and curved surface area of a hemisphere having 2 cm diameter?
(a) 2å…€ sq cm
(b) 3å…€ sq cm
(c) å…€ sq cm
(d) 4å…€ sq cm
(e) None of the above
Answer:- (c) å…€ sq cm
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