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

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#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 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 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
= 22 x [(4)2 – (3)2] x 21 cm3
7
= 22 x 7 x 1 x 21 cm3
7
= 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
= 22 x 7 x 75  22 x 7 x 7 cm2
7 7
= [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
finish