Mathmetics

ISBT Mathmetics for all banking PO,Clerk,IBPS PO,Railway,SSC,IAS,OAS Exams

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Q1.
A rectangular container, whose base is square of side 15cm,stands on a horizontal table and holds water up to 3cm from the top. When a cube is  placed in the water and is completely submerged, the water rises to the top and 54cm^3 of water overflows. What is its surface area?
1) 448cm2 2) 464cm2
3) 486cm2 4) 524cm2
5)None of these
Answer : 486cm2
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Q2.
A cylindrical container of height 14 m and base diameter 12 m contains oil. This oil is to be transferred to one cylindrical can, one conical can and a spherical can. The base radius of all the containers is same. The height of the conical can is 6 m. While pouring some oil is dropped and hence only 3/4th of cylindrical can could be filled. How much oil is dropped ?
1) 36 pie m3 2) 48 pie m3
3) 50 pie m3 4) 54 pie m3
5)None of these
Answer : 36 pie m3
Explanation :
Explanations:
Volume of the oil =  22/7x 62 x 14 = 504 x 22/7 m3.
Base radius of all the containers = 7 m
Volume of the spherical can = (4/3) x (22/7)x 63 m3.
Volume of the conical can =  (1/3) x (22/7) x 62 x 6 m3 = 72 x (22/7)
Balance oil = Volume of the cylindrical can 
= 504 (22/7) - 288 (22/7)- 72(22/7) = 144(22/7) m3.
Oil dropped = 1/4 th of the cylindrical can
= 1/4x 144 = 36 (22/7) m3.
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Q3.
A hollow cone is cut by a plane parallel to the base and the upper portion is removed. If the curved surface area of the remainder is 8/9th of the curved surface of the whole cone, what should be the ratio of the line segments into which the cone’s altitude is divided by the plane is given by ?
1) 2 : 3 2) 1 : 3
3) 1 : 2 4) 1 : 4
5)None of these
Answer : 1 : 2
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Q4.
A 5 cm cube is cut into as many 1 cm cubes as possible. What is the ratio of the surface area of the larger cube to that of the sum of the surface areas of the smaller cubes ?
1) 1 : 6 2) 1 : 5
3) 1 : 25 4) 1 : 125
5)None of these
Answer : 1 : 5
Explanation :
The volume of the larger cube = 53 = 125 cm3.
The volume of each of the smaller cubes = 13 = 1 cm3
         Therefore, one would get 125 smaller cubes.
The surface area of the larger cube = 6a2 = 6(52) = 6  25 = 150
The surface area of each of the smaller cubes = 6 (12) = 6.
Therefore, surface area of all of the 125, 1 cm3 cubes = 125  6 = 750.
Therefore, the required ratio = 150 : 750 = 1 : 5
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Q5.
What is the ratio of the volume of the cube to that of the  sphere which can fit inside the cube ?
1) 3 : 4 2) 21 : 11
3) 11 : 25 4) 4 : 3
5)None of these
Answer : 21 : 11
Explanation :
Let the side of the cube be ‘a’ 
Volume of the cube = a3
Diameter of the sphere = a

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Q6.
The radius of a right circular cylinder is decreased by 5% but its height is increased by 10%. What is the percentage change in its volume ?
1) -0.25% 2) -0.625%
3) -0.725% 4) 1.25%
5)None of these
Answer : -0.725%
Explanation :
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Q7.
The volume of a cuboids is twice the volume of a cube. If the dimensions of the cuboids are 9 cm and, 8 cm and 6 cm, what should be the total surface area of the cube ?
1) 72 cm2 2) 216 cm2
3) 432 cm2 4) 108 cm2
5)None of these
Answer : 216 cm2
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Q8.
If the volumes of two cones are in the ratio of 1:4 and their diameters are in the ratio of 4:5, then what should be the ratio of their heights ?
1) 9:64 2) 27:64
3) 25:64 4) 16:25
5)None of these
Answer : 25:64
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Q9.
A cube of edge 20 cm is completely immersed in a rectangular vessel containing water. If the dimensions of the base of the vessel are 20 cm by 40 cm, the rise in water level will be -.
1) 5 cm 2) 8 cm
3) 10 cm 4) 12 cm
5)None of these
Answer : 10 cm
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Q10.
A circular cylindrical iron piece of radius 14 cm & height 20 cm is molded into a solid cone with the same radius of the base. What is the height of the cone ?
1) 36cm 2) 40cm
3) 60cm 4) 48cm
5)None of these
Answer : 60cm
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