**GSEB Solutions for Class 7 Mathematics – Volume (English Medium)**

GSEB SolutionsMathsScience

**Exercise **

**Solution 1:**

- 1 kilolitre = 1000 litre
- 1000 cu cm = 1000 mililitre

1 cu cm = 1 ml

1000 cu cm = 1 × 1000 mililitre - 1 cu m = 1000 litre

1 cu m = 100 × 100 × 100 = 10,00,000 ml

10,00,000 ml = 1000 litre …(1000 ml = 1 litre) - 1 cu cm = 1 mililitre
- 1 litre = 1000 cu cm

1 litre = 1000 ml

1 ml = 1 cu cm

1000 ml = 1000 cu cm - 4 cu m = 40,00,000 cu cm

1 cu m = 10,00,000 cu cm

4 cu m = 40,00,000 cu cm - 8 litre = 8,000 cu cm

1 litre = 1000 cu cm

8 litre = 8000 cu cm - 1 cu m = 1 kilolitre

1 cu m = 10,00,000 ml …(1 cu cm = 1 ml)

1 cu m = 1000 litre …(1000 ml = 1 litre)

1 cu m = 1 kilolitre …(1000 litre = 1 kilolitre) - Formula to find volume of a cube is l3
- Formula to find volume of cuboid is l × b × h

**Solution 2:**

**Solution 3:**

Given :

Length of the cuboidal tank = 20 m

Breadth of the cuboidal tank = 15 m

Height of the cuboidal tank = 2 m

Volume of a cuboid = l × b × h

∴ Volume of the cuboidal tank = (20 × 15 × 2) m^{3}

= 600 m^{3}

Thus, the volume of a cuboidal tank is 600 m^{3}.

*The question has been rectified.

**Solution 4:**

Given:

Length of the cuboidal cement block = 30 cm

Breadth of the cuboidal cement block = 23 cm

Height of the cuboidal cement block = 12 cm

Volume of a cuboid = l × b × h

∴ Volume of the cuboidal cement block = (30 × 23 × 12) cm^{3}

= 8280 cm^{3}

Thus, the volume of the cuboidal cement block is 8280 cm^{3}.

*The question has been rectified.

**Solution 5:**

Given:

Length of the cuboidal salt-pan = 30 m

Breadth of the cuboidal salt-pan = 10 m

Height (depth) of the cuboidal salt-pan = 10 cm = 0.10 m

Volume of a cuboid = l × b × h

∴ Volume of cuboidal salt-pan = (30 × 10 × 0.10) m^{3}

= 30 m^{3}

Thus, the volume of the cuboidal salt-pan is 30 m^{3}.

To find the capacity of tank, convert the volume of the tank (30 m^{3}) into litres.

Volume of 1 m^{3} = 1000 litres

∴ 30 m^{3} = (30 × 1000) = 30,000 litres.

Hence, 30,000 litres of sea water can be contained in the salt-pan.

**Solution 6:**

Given:

Length of the cubical tank = 3 m

Volume of a cube = l^{3}

∴ Volume of cubical tank = (3 × 3 × 3) m^{3}

= 27 m^{3}

Hence, Volume of the cubical tank is 27 m^{3}

To find the capacity of tank, convert the volume of the tank, 27 m^{3} into litres.

Volume of 1 m^{3} = 1000 litres

∴ 27 m^{3} = (27 × 1000) = 27,000 litres.

Hence, 27,000 litres of water can be stored in the tank.

**Solution 7:**

**Solution 8:**

**Solution 9:**

**Practice – 1**

**Solution 1:**

Let ‘l’ be the length of the cube.

Volume of a cube = length × length × length = l^{3}

∴ Volume of a cube of length 20 cm

= (20 × 20 × 20) cm^{3}

= 8000 cm^{3}

Hence, the volume of the cube is 8000 cm^{3}.

**Solution 2:**

The box is cuboid in shape.

Let ‘l’ be the length, ‘b’ be the breadth and ‘h’ be the height of the cuboid.

Volume of a cuboid = l × b × h

∴ Volume of the cuboid with dimensions 2 metre × 3 metre × 1 metre

= (2m × 3m× 1m)

= 6 m^{3}

Hence, the volume of the cuboidal box is 6 m^{3}.

**Solution 3:**

Let ‘l’ be the length of the cube.

Volume of a cube = length × length × length = l^{3}

∴ Volume of a cube of length 12 cm

= (12 × 12 × 12) cm^{3}

= 1728 cm^{3}

Hence, the volume of the given cube is 1728 cm^{3}.

**Solution 4:**

Let ‘l’ be the length, ‘b’ be the breadth and ‘h’ be the height of the cuboid.

Volume of a cuboid = l × b × h

∴ Volume of given cuboid

= (10 × 8 × 6) m^{3}

= 480 m^{3}

Hence, the volume of the cuboid is 480 m^{3}.

*The question has been rectified.

**Solution 5:**

Let ‘l’ be the length of the cube.

Volume of a cube = length × length × length = l^{3}^{
}

∴ Volume of a cubic stone of length 40 cm

= (40 × 40 × 40) cm^{3}

= 64000 cm^{3}

Hence, the volume of the cube is 64,000 cm^{3}.

**Solution 6:**

Volume of a cuboid = l × b × h

∴ Volume of the cuboidal brick of length 24 cm, breadth 10 cm and height 8 cm

= (24 × 10 × 8) cm^{3}

= 1920 cm^{3}

Hence, the volume of the brick is 1920 cm^{3}.

**Solution 7:**

Volume of a cuboid = l × b × h

∴ Volume of a cuboidal compass box of length 16 cm, breadth 4 cm and height 2 cm

= (16 × 4 × 2) cm^{3}

= 128 cm^{3}

Hence, the volume of the compass box is 128 cm^{3}.

**Solution 8:**

Volume of a cuboid = l × b × h

∴ Volume of a cuboidal tank of length 3 m, breadth 2 m and height 6 m

= (3 × 2 × 6) m^{3}

= 36 m^{3}

Hence, the volume of the tank is 36 m^{3}.

**Practice – 2**

**Solution 1:**

**Solution 2:**

**Solution 3:**

Volume of a cuboid = l × b × h

∴ Volume of the cuboidal tank = 3 m × 2 m × 2 m = 12 m^{3}

To find the capacity of the tank, convert the volume of the tank 12 m^{3} into litres.

Now, 1 m^{3} = 1000 litres

∴ 12 m^{3} = (12 × 1000) = 12,000 litres.

Hence, 12,000 litres of water can be stored in the tank.

**Solution 4:**

**Solution 5:**