Quantitative Aptitude
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Question 1
A hall is 15 m long and 12 m broad. If the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls, the volume of the hall is:
Correct Answer: Option C
2(15 + 12) x h = 2(15 x 12)
 h = |
180 | m = | 20 | m. |
| 27 | 3 |
 Volume = |
 |
15 x 12 x | 20 |  m3 |
= 1200 m3. |
| 3 |
Question 2
A hollow iron pipe is 21 cm long and its external diameter is 8 cm. If the thickness of the pipe is 1 cm and iron weighs 8 g/cm3, then the weight of the pipe is:
Correct Answer: Option B
External radius = 4 cm,
Internal radius = 3 cm.
| Volume of iron |
|
||||||
|
|||||||
| = 462 cm3. |
Weight of iron = (462 x 8) gm = 3696 gm = 3.696 kg.
Question 3
A metallic sheet is of rectangular shape with dimensions 48 m x 36 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 8 m, the volume of the box (in m3) is:
Correct Answer: Option B
Clearly, l = (48 - 16)m = 32 m,
b = (36 -16)m = 20 m,
h = 8 m.
Volume of the box = (32 x 20 x 8) m3 = 5120 m3.
Question 4
A boat having a length 3 m and breadth 2 m is floating on a lake. The boat sinks by 1 cm when a man gets on it. The mass of the man is:
Correct Answer: Option B
| Volume of water displaced | = (3 x 2 x 0.01) m3 |
| = 0.06 m3. |
Mass of man
| = Volume of water displaced x Density of water | |
| = (0.06 x 1000) kg | |
| = 60 kg. |
Question 5
66 cubic centimetres of silver is drawn into a wire 1 mm in diameter. The length of the wire in metres will be:
Correct Answer: Option A
Let the length of the wire be h.
| Radius = | 1 | mm | = | 1 | cm. | Then, |
| 2 | 20 |
| |
22 | x | 1 | x | 1 | x h = 66. |
| 7 | 20 | 20 |
| h = |
|
66 x 20 x 20 x 7 | |
= 8400 cm = 84 m. |
| 22 |
Question 6
In a shower, 5 cm of rain falls. The volume of water that falls on 1.5 hectares of ground is:
Correct Answer: Option B
1 hectare = 10,000 m2
So, Area = (1.5 x 10000) m2 = 15000 m2.
| Depth = | 5 | m | = | 1 | m. |
| 100 | 20 |
| Volume = (Area x Depth) = |
|
15000 x | 1 | m3 |
|
| 20 |
= 750 m3.
Question 7
A cistern 6m long and 4 m wide contains water up to a depth of 1 m 25 cm. The total area of the wet surface is:
Correct Answer: Option A
Area of the wet surface:
| = [2(lb + bh + lh) - lb] | |
| = 2(bh + lh) + lb | |
| = [2 (4 x 1.25 + 6 x 1.25) + 6 x 4] m2 | |
| = 49 m2. |
Question 8
50 men took a dip in a water tank 40 m long and 20 m broad on a religious day. If the average displacement of water by a man is 4 m3, then the rise in the water level in the tank will be:
Correct Answer: Option B
Total volume of water displaced = (4 x 50) m3 = 200 m3.
| Rise in water level = |
|
200 | m 0.25 m |
| 40 x 20 |
= 25 cm.
Question 9
The slant height of a right circular cone is 10 m and its height is 8 m. Find the area of its curved surface.
A
30
m2
m2B
40 m2
m2C
60 m2
m2D
80 m2
m2
Correct Answer: Option C
l = 10 m,
h = 8 m.
So, r = l2 - h2 = (10)2 - 82 = 6 m.
Curved surface area = rl = ( x 6 x 10) m2 = 60 m2.
Question 10
A right triangle with sides 3 cm, 4 cm and 5 cm is rotated the side of 3 cm to form a cone. The volume of the cone so formed is:
A
12 cm3
cm3B
15 cm3
cm3C
16 cm3
cm3D
20 cm3
cm3
Correct Answer: Option A
Clearly, we have r = 3 cm and h = 4 cm.
| Volume = |
1 | r2h = |
|
1 | x x 32 x 4 |
cm3 |
|
| 3 | 3 |
cm3.