GSEB Solutions for Class 7 Mathematics – Volume

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

GSEB SolutionsMathsScience
Exercise 

Solution 1:

1.  1 kilolitre = 1000 litre
2. 1000 cu cm = 1000 mililitre
   1 cu cm = 1 ml
   1000 cu cm = 1 × 1000 mililitre
3.  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)
4.  1 cu cm = 1 mililitre
5.  1 litre = 1000 cu cm
   1 litre = 1000 ml
   1 ml = 1 cu cm
   1000 ml = 1000 cu cm
6.  4 cu m = 40,00,000 cu cm
   1 cu m = 10,00,000 cu cm
   4 cu m = 40,00,000 cu cm
7.  8 litre = 8,000 cu cm
   1 litre = 1000 cu cm
   8 litre = 8000 cu cm
8.  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)
9.  Formula to find volume of a cube is l3
10.  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) m³
= 600 m³
Thus, the volume of a cuboidal tank is 600 m³.
*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) cm³
= 8280 cm³
Thus, the volume of the cuboidal cement block is 8280 cm³.
*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) m³
= 30 m³
Thus, the volume of the cuboidal salt-pan is 30 m³.
To find the capacity of tank, convert the volume of the tank (30 m³) into litres.
Volume of 1 m³ = 1000 litres
∴ 30 m³ = (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 = l³
∴ Volume of cubical tank = (3 × 3 × 3) m³
= 27 m³
Hence, Volume of the cubical tank is 27 m³
To find the capacity of tank, convert the volume of the tank, 27 m³ into litres.
Volume of 1 m³ = 1000 litres
∴ 27 m³ = (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 = l³
∴ Volume of a cube of length 20 cm
= (20 × 20 × 20) cm³
= 8000 cm³
Hence, the volume of the cube is 8000 cm³.

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 m³
Hence, the volume of the cuboidal box is 6 m³.

Solution 3:

Let ‘l’ be the length of the cube.
Volume of a cube = length × length × length = l³
∴ Volume of a cube of length 12 cm
= (12 × 12 × 12) cm³
= 1728 cm³
Hence, the volume of the given cube is 1728 cm³.

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) m³
= 480 m³
Hence, the volume of the cuboid is 480 m³.
*The question has been rectified.

Solution 5:

Let ‘l’ be the length of the cube.
Volume of a cube = length × length × length = l³

∴ Volume of a cubic stone of length 40 cm
= (40 × 40 × 40) cm³
= 64000 cm³
Hence, the volume of the cube is 64,000 cm³.

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) cm³
= 1920 cm³
Hence, the volume of the brick is 1920 cm³.

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) cm³
= 128 cm³
Hence, the volume of the compass box is 128 cm³.

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) m³
= 36 m³
Hence, the volume of the tank is 36 m³.

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 m³
To find the capacity of the tank, convert the volume of the tank 12 m³ into litres.
Now, 1 m³ = 1000 litres
∴ 12 m³ = (12 × 1000) = 12,000 litres.
Hence, 12,000 litres of water can be stored in the tank.

Solution 4:

Solution 5: