**” Volumes and Surface Area”.**Most of the students think that they are comfortable with these question but some times even a minor mistake can make a huge difference. So go through these formula and remember it in future.These questions will be helpful for SSC Exams.

**Cuboid**:

1. Volume = (l x b x h) cubic units.

2. Surface area = 2(lb + bh + lh) sq. units.

3. Diagonal = √l^2 + b^2 + h^2 units.

**2. Cube :**

Let each edge of a cube be of length a. Then,

1. Volume = a^3 cubic units

3. Diagonal =√ 3a units.

**Questions on Above Formula**

**1**.A cube of edge 5 cm is cut into cubes of each edge 1 cm. The ratio of the total surface area of one of the small cubes to that of the large cube is equal to

A.1 : 5

B.1 : 25

C.1 : 125

D.1 : 625

**2**.The cost of painting the whole surface area of a cube at the rate of 13 paise per Sq.cm is Rs. 343.98. Then the volume of the cube is

A.8500 cm^3

B.9000 cm^3

C.9250 cm^3

D.9261 cm^3

**3.**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 man is

A.12 kg

B.60 kg

C.72 kg

D.96 kg

**4.**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?

A.5600

B.6000

C.6400

D.7200

**5.**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:

A.720

B.900

C.1200

D.1800

**6.**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:

A.3.6 kg

B.3.696 kg

C.36 kg

D.36.9 kg

**7.**A right triangle with sides 3 cm, 4 cm and 5 cm is rotated about the side of 3 cm to form a cone. The volume of the cone so formed is

A.12pie cm^3

B.15pie cm^3

C.16pie cm^3

D.20pie cm^3

**8.**The surface area of a sphere is same as the curved surface area of a right circular cylinder whose height and diameter are 12 cm each. The radius of the sphere is

A.3 cm

B.4 cm

C.6 cm

D.8 cm

**9.**Five equal cubes, each of side 5 cm, are placed adjacent to each other. The volume of the new solid formed will be

A.125 cm^3

B.625 cm^3

C.15525cm^3

D.1225cm^3

**10**.An iron cubes of side 10 cm is hammered into a rectangular sheet of thickness 0.5 cm. If the sides of the sheet are in the ratio 1 : 5 the sides are

A.10 cm, 50 cm

B.20 cm, 100 cm

C.40 cm, 200 cm

D.None of these

**Answer With Explanations:**

1.(6x1x1 / 6x5x5)

‹=› 1/ 25

‹=› 1 : 25.

2.Surface area = (34398 / 13)

‹=›2646cm^3

‹=›6a^2= 2646

‹=›a^2= 441

‹=›a = 21.

So,volume =(21x21x21)cm^3= 9261cm^3

3.Volume of water displaced = (3 x 2 x 0.01)m^3

= 0.06m3.

Mass of man =Volume of water displaced ×Density of water

= (0.06×1000) kg

= 60 kg.

4.Number of bricks = Volume of the wall/Volume of 1 brick

=(800x600x22.5 /25×11.25×6)

= 6400

5. 2(15 + 12) ×h = 2(15 x 12)

‹=›h= 180/27 m

= 20/3m

Volume = (15×12×20/3)m^3

‹=›1200 m^3.

6. External radius = 4 cm,

Internal radius = 3 cm.

Volume of iron =(22/7×(42)-(32)×21)cm^3

= (22/7×7 ×1×21)cm^3

= 462 cm^3.

7.(a)

8. 4?R^2= 2?6×12

R^2 = (6×12/2)= 36

R = 6 cm.

9.The new solid formed is a cuboid of length 25 cm, breadth 5 cm and height 5 cm

Volume = (25x5x5)cm^3

‹=›625cm^3

10.Let the sides of the sheet be x and 5x.

Then,volume of the sheet= volume of the cube

‹=› x × 5x ×1/2

‹=› 10×10×10

‹=› 5x^2= 2000

‹=› x^2= 400

‹=› x = 20.

The sides are 20 cm and 100 cm.

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