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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:

gseb-solutions-class-7-mathematics-volume-2.1
gseb-solutions-class-7-mathematics-volume-2.2

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:

gseb-solutions-class-7-mathematics-volume-7

Solution 8:

gseb-solutions-class-7-mathematics-volume-8

Solution 9:

gseb-solutions-class-7-mathematics-volume-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:

gseb-solutions-class-7-mathematics-volume-1

Solution 2:

gseb-solutions-class-7-mathematics-volume-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:

gseb-solutions-class-7-mathematics-volume-4

Solution 5:

gseb-solutions-class-7-mathematics-volume-5

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