Mathmetics
ISBT Mathmetics for all banking PO,Clerk,IBPS PO,Railway,SSC,IAS,OAS Exams
Q1. | The ratio between the curved surface area and the total surface area is 2:3 and the total surface is 924 cm2. What is the volume of the cylinder? |
| 1) | 2156 cm3 | 2) | 2183 cm3 |
| 3) | 2492 cm3 | 4) | 2592 cm3 |
| 5) | None of these | ||
Answer : 2156 cm3
Explanation :
Explanation :
Total surface area = 924 cm2
Then, the curved surface area = (924 /3) ×2 = 308 ×2 616 cm2
Area of the base = (924- 616)/ 2 = 154cm2.
Let, the radius of base = r and pie r2 = 154 cm2
So, r2 = (154× 7) / 22 = 49
or r = 7 cm.
Then, 2pie r = 2× (22/ 7)× 7 44 cm.
Hence, surface area = 2pie rh = 616 cm2
Or, 2× (22 /7)× 7 h= 616
or h = (616/ 44)
Volume = pie r2h = 154 × (616 /44) cm3 = 2156 cm3
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Q2. | A solid wooden toy is in the shape of a right circular cone mounted on the base of a hemisphere. If the radius of the hemisphere is 4.2 cm and the total height of the toy is 10.2 cm, find the volume of the wood needed to construct another such toy. |
| 1) | 104 cm3 | 2) | 162 cm3 |
| 3) | 427 cm3 | 4) | 266 cm3 |
| 5) | None of these | ||
Answer : 266 cm3
Explanation :
Explanation :
The total volume of the wood is the sum of the volumes of the hemisphere and the right circular cone.
(â…“ x 22/7 x 4.2 x 4.2 x 10.2 ) + ( â…” x 22/7 x 4.2 x4.2 x4.2)
=22 x 0.84 x 14.4 =266.112 cm^3
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Q3. | 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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Q4. |
|
| 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 :
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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Q5. |
|
| 1) | 2 : 3 | 2) | 1 : 3 |
| 3) | 1 : 2 | 4) | 1 : 4 |
| 5) | None of these | ||
Answer : 1 : 2
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Q6. |
|
| 1) | 1 : 6 | 2) | 1 : 5 |
| 3) | 1 : 25 | 4) | 1 : 125 |
| 5) | None of these | ||
Answer : 1 : 5
Explanation :
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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Q7. |
|
| 1) | 3 : 4 | 2) | 21 : 11 |
| 3) | 11 : 25 | 4) | 4 : 3 |
| 5) | None of these | ||
Answer : 21 : 11
Explanation :
Explanation :
Let the side of the cube be ‘a’
Volume of the cube = a3
Diameter of the sphere = a
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Q8. | 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 :
Explanation :
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Q9. |
|
| 1) | 72 cm2 | 2) | 216 cm2 |
| 3) | 432 cm2 | 4) | 108 cm2 |
| 5) | None of these | ||
Answer : 216 cm2
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Q10. |
|
| 1) | 9:64 | 2) | 27:64 |
| 3) | 25:64 | 4) | 16:25 |
| 5) | None of these | ||
Answer : 25:64
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