# Volume Calculation - Solved Examples

Q 1 - The diagonal of a cube is 12√6m .Find its surface area.

A - 1624 m2

B - 1728 m2

C - 2564 m2

D - 1254√2m2

Explanation

```Let the edge of the cube be X.
√(3 )X=12√(6)
⇒ X=12√(2)
Surface area = 6X2 = (6 x 12√(2) x12√(2)) m2 ≡ 1728 m2.
```

Q 2 - The surface area of a cube is 1728 cm2. Find its volume.

A - 3456√2 cm3

B - 256√2 cm3

C - 125√2 cm3

D - 144√2 cm3

Explanation

```Let the edge of the cube be X. Then,
6X2 = 1728
⇒ X2 = 288
⇒ X = 12√2 cm.
Volume = X3 = (12√2)3 cm3
= 3456√2 cm3.
```

Q 3 - Find the number of bricks, each measuring 24 cm x 12 cm x 8 cm, required to construct a wall 24 m long, 8m high and 60 cm thick.

A - 12500

B - 11500

C - 12000

D - 10000

Explanation

```Volume of the wall = (1800 x 600 x 90) cm3.
Volume of 1 brick = (36 x 18 x 12) cm3.
Number of bricks=((1800 x 600 x 90)/( 36 x 18 x 12)=12500
```

Q 4 - A right triangle with sides 6 cm, 8 cm and 10 cm is rotated the side of 6 cm to form a cone. The volume of the cone so formed is:

A - 96 cm3

B - 96π cm3

C - 96/π cm3

D - 96π3

Explanation

```We have R = 6 cm and H = 8 cm.
Volume = (1/3)πR2H= (1/3)πx62x8=96π cm3
```

Q 5 - A room is 30 m long and 24 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:

A - 96 m3

B - 960 m3

C - 9600 m3

D - 96000 m3

Explanation

```Let the height be H
2(30 + 24) x H = 2(30 x 24)
⇒ H=(2(30 x 24))/(2(30 + 24))=(30 x 24)/54=40/3 m
⇒ Volume = 30 x 24 x 40/3 = 9600 m3
```

Q 6 - A hollow steel pipe is 42 cm long and its external diameter is 16 cm. If the thickness of the pipe is 2 cm and steel density weighs 12 g/cm3, then the weight of the pipe is:

A - 51.744 kg

B - 45.834 kg

C - 48.225 kg

D - 55.565 kg

Explanation

```External radius = 8 cm,
Volume of steel = ( π x (82-62) x42) =1176 π cm3
Weight of steel = (1176 π x 12) gm = 51744 gm = 51.744 kg.
```

Q 7 - Find the area of right circular cone curved surface if slant height is 20 m and height is 16 m.

A - 100π m2

B - 200π m2

C - 320π m2

D - 240π m2

Explanation

```L = 20 m, H = 16 m.
So, R = √(L2-H2) = √(202-162) = 12 m.
⇒ Curved surface area = πRL = (π x 12 x 20) m2 = 240π m2.
```

Q 8 - Find the volume & curved surface area of a cylinder with diameter of base 14 cm and height 60 cm.

A - 4640cm3 & 1340 cm2

B - 9240cm3 & 1340 cm2

C - 4640cm3 & 2640 cm2

D - 9240cm3 & 2640 cm2

Explanation

```Volume =  πR2H= π x 72 x 60 = 9240	cm3
Curved surface area = 2πRH = (2 π x 7 x 60) cm2 =2640 cm2
```

Q 9 - If the volume of a cylindrical tank is 3696 m3 and the diameter of its base is 28 m, then find the depth of the tank.

A - 5 m

B - 6 m

C - 8 m

D - 14 m

Explanation

```Let the depth of the tank be H meters. Then,
Volume =  πR2H= π x 142 x H = 3696 m3
⇒ H=6 m
```

Q 10 - How many steel rods, each of length 14 m and diameter 4 cm can be made out of 1.76 cm3 of steel?

A - 80

B - 100

C - 110

D - 120

Explanation

```Volume of 1 rod = (( 22/7) x (2/100) x (2/100) x 14 ) m3= 11/625 m3
Volume of steel = 1.76 m3
Number of rods = (1.76 x 625/11) = 100.
```

Q 11 - Find the volume and surface area of a Box 32 m long, 28 m broad and 14 m high.

A - 12544 m3 & 3472 m2

B - 12500 m3 & 3472 m2

C - 12600 m3 & 3400 m2

D - 12000 m3 & 3000 m2

Explanation

```Volume = (32 x 28 x 14) m3 = 12544 m3.
Surface area = [2 (32 x 28 + 28 x 14 + 32 x 14)] m2 = (2 x 1736) m2 = 3472 m2.
```

Q 12 - Find the length of the longest pole that can be placed in a room 24 m long 16 m broad and 18 m high.

A - 34 m

B - 24 m

C - 14 m

D - 4 m

Explanation

```Length of the longest pole=√(242+162+182)=34 m
```

Q 13 - A wheel makes 2000 revolutions in covering a distance of 44 km. Find the radius of the wheel.

A - 12 m

B - 14 m

C - 13 m

D - 15 m

Explanation

```Distance covered in one revolution = ((44 X 2000)/1000) = 88m.
2πR = 88
2 x (22/7) x R = 88
⇒ R = 88 x (7/44) = 14 m.
```

Q 14 - A rectangular block 35 cm x 42 cm x 70 cm is cut up into an exact number of equal cubes. Find the least possible number of cubes.

A - 300

B - 200

C - 100

D - 50

Explanation

```Volume of the block = (35 cm x 42 cm x 70 cm) cm3 = 300x73 cm3.
Side of the largest cube = H.C.F. of 35 cm , 42 cm and 70 cm = 7 cm.
Volume of this cube = (7 x 7 x 7) cm3 = 73 cm3.
Number of cubes = 300x73/73 = 300.
```

Q 15 - Two cubes have their volumes in the ratio 8: 125. Find the ratio of their surface areas.

A - 4:25

B - 2:25

C - 1:25

D - 3:25

Explanation

```Let their edges be X and Y. Then,
X3/Y3 = 8/125 (or) (X/Y)3 = (2/5)3 (or) (X/Y) = (2/5).
Ratio of their surface area = 6X2/6Y2 = X2/Y2 = (X/Y)2 = 4/25, i.e. 4:25.
```

Q 16 - Find the volume and surface area of a sphere of radius 21 cm.

A - 38008 cm3 & 5444 cm2

B - 38808 cm3 & 5544 cm2

C - 38888 cm3 & 4544 cm2

D - 30008 cm3 & 5544 cm2

Explanation

```Volume = (4/3)πr3 =(4/3)*(22/7)*(21)*(21)*(21) cm3 = 38808 cm3.
Surface area = 4πr2 =(4*(22/7)*(21)*(21)) cm2 = 5544 cm2
```

Q 17 - The volume of a wall, 10 times as high as it is broad and 16 times as long as it is high, is 25.6 m3. Find the breadth of the wall.

A - ∛2/5 m

B - ∛5/2 m

C - ∛5/3 m

D - ∛3/2 m

Explanation

```Let the breadth of the wall be X meters.
Then, Height = 10X meters and Length = 160X meters.
X x 10X x 160X = 25.6
⇒ X3=25.6/1600
=2/125
⇒X = ∛2/5 m
```

Q 18 - Two metallic right circular cones having their heights 4.1 cm and 4.3 cm and the radii of their bases 2.1 cm each have been melted together and recast into a sphere. Find the diameter of the sphere.

A - 2 cm

B - 3 cm

C - 4 cm

D - 5 cm

Explanation

```Volume of sphere = Volume of 2 cones
= (1/3 π x (12) x 2.2 + 1/3 π x (1)2 x 1.8) =	4/3 π
Let the radius of sphere be R
4/3 π R3 = 4/3 π or R = 1cm
Hence , diameter of the sphere = 2 cm
```

Q 19 - The diameter of garden roller is 2.8 m and it is 3 m long. The area covered by the roller in 10 revolutions is?

A - 132 m2

B - 264 m m2

C - 132/5 m2

D - 264/5 m2

Explanation

```Curved surface area of roller = (2 π R H) = 2 x π x 1.4 x 3=132/5.
Area covered by the roller = 10 x (132/5) =264 m2
```

Q 20 - The curved surface area of a cylindrical pillar is 440 m2 and its volume is 1540 m3. Find the ratio of its diameter to its height.

A - 7:5

B - 6:5

C - 5:7

D - 6:7

```Curved surface area = (2 π R H) = 440