Instructions: This Monk test contains JK Bank Volume and Surface Problems with answer. This will help you in JK bank exam preparation.
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Results
#1. 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:
Answer: Option A
Explanation:
Clearly, we have r = 3 cm and h = 4 cm.
 Volume = |
1 |  r2h = |
 |
1 | x x 32 x 4 |
 cm3 |
= 12 cm3. |
| 3 | 3 |
#2. In a shower, 5 cm of rain falls. The volume of water that falls on 1.5 hectares of ground is:
Answer: Option B
Explanation:
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 |
= 750 m3. |
| 20 |
#3. 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:
Answer: Option C
Explanation:
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 |
#4. 66 cubic centimetres of silver is drawn into a wire 1 mm in diameter. The length of the wire in metres will be:
Answer: Option A
Explanation:
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 |
#5. 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:
Answer: Option B
Explanation:
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.
#6. 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:
Answer: Option B
Explanation:
| 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. |
#7. 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:
Answer: Option B
Explanation:
Total volume of water displaced = (4 x 50) m3 = 200 m3.
| Rise in water level = |
|
200 | m 0.25 m = 25 cm. |
| 40 x 20 |
#8. The slant height of a right circular cone is 10 m and its height is 8 m. Find the area of its curved surface.
Answer: Option C
Explanation:
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.
#9. 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:
Answer: Option A
Explanation:
| 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. |
#10. 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 m^3) is:
Answer: Option B
Explanation:
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.
#11. The curved surface area of a cylindrical pillar is 264 m^2 and its volume is 924 m^3. Find the ratio of its diameter to its height.
Answer: Option B
Explanation:
| r2h |
= | 924 | r = |
|
924 | x 2 | |
= 7 m. |
| 2rh |
264 | 264 |
| And, 2rh = 264 h = |
|
264 x | 7 | x | 1 | x | 1 | |
= 6m. |
| 22 | 2 | 7 |
| Required ratio = |
2r | = | 14 | = 7 : 3. |
| h | 6 |
#12. A cistern of capacity 8000 litres measures externally 3.3 m by 2.6 m by 1.1 m and its walls are 5 cm thick. The thickness of the bottom is:
Answer: Option B
Explanation:
Let the thickness of the bottom be x cm.
Then, [(330 – 10) x (260 – 10) x (110 – x)] = 8000 x 1000
320 x 250 x (110 – x) = 8000 x 1000
| (110 – x) = |
8000 x 1000 | = 100 |
| 320 x 250 |
x = 10 cm = 1 dm.
#13. What is the total surface area of a right circular cone of height 14 cm and base radius 7 cm?
Answer: Option C
Explanation:
h = 14 cm, r = 7 cm.
So, l = (7)2 (14)2 = 245 = 75 cm.
| Total surface area |
= rl r2 |
|||||||||
|
||||||||||
| = [154(5 1)] cm2 | ||||||||||
| = (154 x 3.236) cm2 | ||||||||||
| = 498.35 cm2. |
#14. A large cube is formed from the material obtained by melting three smaller cubes of 3, 4 and 5 cm side. What is the ratio of the total surface areas of the smaller cubes and the large cube?
Answer: Option C
Explanation:
Volume of the large cube = (33 43 53) = 216 cm3.
Let the edge of the large cube be a.
So, a3 = 216 a = 6 cm.
| Required ratio = |
|
6 x (32 42 52) | |
= | 50 | = 25 : 18. |
| 6 x 62 | 36 |
#15. How many bricks, each measuring 25 cm x 11.25 cm x 6 cm, will be needed to build a wall of 8 m x 6 m x 22.5 cm?
Answer: Option C
Explanation:
| Number of bricks = | Volume of the wall | = | |
800 x 600 x 22.5 | |
= 6400. |
| Volume of 1 brick | 25 x 11.25 x 6 |