2. CHAPTER TEXT BOOK LINK
https://drive.google.com/file/d/1Qs2XM7HSM
OnO-19KDbUutEmsuEfojD_h/view?ts=5eaf04c0
CLASS-IV, CHAPTER- VOLUME,
PRIMARY MATHEMATICS (DAV)
3. LEARNING OBJECTIVES
Understanding the concept of volume
Understanding the measurment of volume
Understanding the units of volume
Measuring the volume of a cuboid and a cube.
Finding the volume of a cube
Finding the volume of a cuboid
Solving word problems based on volume
5. Now you can say-
1. Which of the following objects occupies more space ?
Football or cricket ball
2. Which of the following fruits occupies more space ?
Water melon or Lemmon
6. 3. Which of the following objects occupies more space ?
Book or pencil
4. Which of the following animals occupies more space ?
Elephant or Lion
7. In No-1, the football occupies more space than the cricket ball.
So the football has more volume than the cricket ball.
In No-2, the water melon occupies more space than the lemon.
So the water melon has more volume than the lemon.
In No-3, The pencil occupies less space than the book.
So the pencil has less volume the book.
In No-4, the elephant occupies more space than the lion.
So the elephant has more volume than the lion.
Remember: Amount of space occupied an object is called its
volume.
8. Take two boxes of same shape and same size. But one
is empty and another is full of books. Which has more
volume ?
Empty or full objects of same size and shape have the same
volume.
Volume of an object depends on the outer physical size.
9. Worksheet-1
1. Which of the following has more volume ?
a. Cricket ball or table tennis ball
b. Dice or brick
c. Potato or pumpkin
d. Room and almirah
e. The earth or the moon
2. In each of the following pairs which objects has lesser volume ?
i
i
ii
ii
i ii
10. Worksheet-1
3. Which of the following are true?
(a) A cricket ball and a football have the same volume .
(b) A empty chalk box has less volume than a chalk box of same shape and
size and full of chalks.
(c ) Two oil cans of same size , one empty and one full of oil have the same
volume.
(d) A half litre of polypack of milk and a one litre polypack of milk have the
same volume.
12. Let us measure the volume of this empty box.
Now fill this box with marbles to find its volume.
So volume of this box = 32 marbles.
We have used 32 marbles to
fill this box.
13. Here, some spaces is left between
the marbles.
So volume of the box cannot be 40 marbles. We
need an accurate unit for measuring the volume.
Let us fill the box with cubes to find its
volume.
14. Here we have used 20 cubes to fill
the box.
So volume of this box = 20 cubes.
Here, no spaces is left between the
cubes.
15. If we use the cubes to fill the box, no place will be left
between the cubes and inside the box. So we choose a
cube as the best unit for measuring volume.
A cube is the best unit to measure the volume.
Why do we use cubes to measure the volume ?
16. The volume of a solid is measured by
counting the number of unit cubes it
contains.
17. Let us measure the volume of the
following solids in terms of the unit of
volume (Cubes)
4 cubes
8 cubes
8 cubes
12 cubes
18. Let us measure the volume of the following structures in
terms of the unit of volume (Cubes)
12 cubes 11 cubes
13 cubes
19. Worksheet-2
1. Find the volume of the following solids in terms of the unit of volume
(cubes)
(a) (b) (c) (d)
2. Which of the following is the unit to measure volume ?
(a) (b) (c)
1 cm
1
cm
1
cm
1 cm
1 cm
1 cm
1
cm
21. 1 cm
1
cm
For finding the
area we divide the
region into
squares.
Similarly, to.
find the volume of a solid
we need to divide it into
cubes
22. In order to find the volume
of this solid let us use cubes
with each edge equal to 1
cm.
So the volume of this solid is
equals to 12 cubic centimetres
or 12 cu.cm
Here, the solid
contains twelve
cubes. Each edge of
the cube is 1 cm
23. The units used to measure volume are-
Cubic millimetre (cu.mm)
Cubic centimetre (cu.cm)
Cubic metre (cu.m)
Here : 1 cu. mm = 1 mm × 1 mm × 1 mm
1 cu. cm = 1 cm × 1 cm × 1 cm
1 cu. m = 1 m × 1 m × 1 m
24. The units of side and volume :
Units of side Units of Volume
Millimetre (mm) Cubic millimetre ( cu. mm)
Centimetre (cm) Cubic millimetre ( cu. mm)
Metre (m) Cubic metre ( cu. m)
27. VOLUME OF A CUBOID
We can also multiply 4 ×2 × 2 =
16 cubic centimetres or 16
cu.cm
The volume of this cuboid can
be measured by counting the
number of cubes of edge 1 cm.
There are 16 cubes in this
cuboid. So the volume of this
cuboid is 16 cubic centimetres
or 16 cu.cm.
1 cm
1
cm
1
c
m
28. VOLUME OF A CUBOID
We know that, This cuboid has-
Length = 4 cm, Breadth = 4 cm
and Height = 2 cm
The volume of this cuboid can
be measured by counting the
number of cubes of edge 1
cm.
There are 32 cubes in this
cuboid. So the volume of this
cuboid is 32 cubic centimetres
or 32 cu.cm.
1 cm
1
cm
1
c
m
We can also multiply 4 × 4 × 2 =
32 cubic centimetres or 32
cu.cm
29. VOLUME OF A CUBOID
Volume of a cuboid = Length × Breadth × Height
Length
B
r
e
a
d
t
h
Height
We can find the volume of the cuboid by
multiplying the Length x Breadth x
Height.
30. CUBE
A Cube is a box shaped solid object
in which all the edges are equal.
Rubik’s Cube
Dice Gift box
Box
Examples of a cube
Edge
Edge
E
d
g
e
31. VOLUME OF A CUBOID
We can also multiply 2 ×2 × 2 = 8
cubic centimetres or 8 cu.cm
The volume of this cube can
be measured by counting the
number of cubes of edge 1
cm.
There are 8 cubes in this cube.
So the volume of this cube is
8 cubic centimetres or 8 cu.cm.
1 cm
1
cm
1
c
m
32. VOLUME OF A CUBE
Volume of a cube = Edge × Edge × Edge
E
d
g
e
Edge
Edge
We can find the volume of a cube by
multiplying the Edge x Edge x Edge.
33. ACTIVITY
1. Measure the dimensions of a
pencil box and find its volume.
Rubik’s Cube
Pencil Box
2 . Measure the dimensions of a Rubik’s
cube and find its volume.
36. Word Problems
Example-1 :
The length, breadth and height of
a book are 12 cm, 8 cm and 6cm
respectively. What is the
volume of the book.
37. Solution
Length of the book = 12 cm
Breadth of the book = 8 cm
Height of the book = 6 cm ( ½ )
Volume of the book = Length× Breadth × Height
= 12 cm × 8 cm × 6 cm
= 576 cu. cm (2 ½ )
The volume of the book is 576 cubic centimetre.
38. Word Problems
Example- 2:
A child playing with building blocks,
which are of the shape of cubes, has
build a structure as shown in the
figure. If the edge of each cube is 3 cm,
find the volume of the structure built
by the child .
Figure
39. Solution
Edge of each cube = 3 cm
Volume of each cube : Edge × Edge × Edge (½ )
Volume of each cube = 3 cm × 3 cm × 3cm = 27 cubic cm = 27 cu.cm.
(1½ )
Number of cubes in the structure- 15 (1)
Therefore volume of the structure= 15 × 27 cubic. cm = 405 cu.cm (1)
40. Word Problems
Example-13:
The length, breadth and height of
a cuboidal water tank are 15 m,
12 m and 8 m respectively. If half
of the tank is filled with water,
find the volume of water in the
tank.
41. Solution
Length of a cuboidal water tank = 15 m
Breadth of a cuboidal water tank =12 m
Height of a cuboidal water tank = 8 m ( ½ )
So volume of the brick is 15 m × 12 m × 8 m = 1440 cu. m ( 2 )
Volume of half of the water tank = 1440 cu.m/2 = 720 cu.m (1½ )
Therefore volume of water in the tank = 720 cu.m
42. Worksheet-3
Solve the following word problems.
1. Find the volume of the following cuboids whose dimensions given below.
(a) Length = 5 cm , breadth = 4 cm, height = 3 cm
(b) Length = 10 cm , breadth = 8 cm, height = 5 cm
(c) Length = 12 m , breadth = 10 m, height = 8 m
2. Find the volume of these cubes whose edges are given below.
(a) 5 cm (b) 8 cm (c) 11 m
3. Find the volume of a brick of length 20 cm, breadth 10 cm and height 7 cm.
4. A dice has edge of 3 cm. Find the volume of the dice.
5. A dictionary has a length 22 cm, breadth 14 cm and height 8 cm. Find the
volume of the dictionary.
6. Find the volume of a sugar grain of edge 1 mm.
43. Students will able to-
Understand the concept of volume.
Understand the measurement of volume.
Understand the units of volume.
Students would be able to-
Develop the ability to measure the volume of a cuboid and a cube.
Find out the volume of a given cuboid and a cube.
Perform numerical skills of solving word problems based on volume
and develop critical thinking and collaboration competencies in the
process.
LEARING OUTCOMES
44. Measuring Volume
VOLUME
Word problems
Units of
Volume
The units of volume are
Cubic millimetre (cu.mm)
Cubic centimetre (cu.cm)
Cubic metre (cu. m)
Volume of a
cuboid and a cube
Volume of a cuboid =
Length ×Breadth × Height
Volume of a cube = Edge ×
Edge × Edge
Concept Map
45. SUB-MATHEMATICS, CLASS-IV, CHAPTER-VOLUME,
WORKSHEET(BASIC)
Choose the correct answer.
1. Amount of space occupied by a solid is called its-
(i) side (ii) area (iii) perimeter (iv) volume
2. Which of the following has the greatest volume?
(i) football (ii) cricket ball (iii) table tennis ball (iv) golf ball
3. The units used to measure volume is-
(i) cu. mm. (ii) cu. cm. (iii) cu. m. (iv) all of these
4. The best unit to measure volume is –
(i) sphere (ii) cuboid (iii) cube (iv) square
5. Volume of a cube of edge 1 m is
(i) 1m (ii) 1 sq. m (iii) 1 cu.m (iv) 3 m
46. Fill in the blanks.
6. Cube is the best unit for measuring ______________.
7. Volume of a cube = Edge × ____________ × ______________
8. Volume of a cuboid = Length × ____________ × ____________
9. Volume of a cube of edge 1 cm is _____________.
10. If a box is filled with 8 cubes of edge 1 cm each, its volume is _________.
Answer the following questions.
11. Find the volume of a cuboid whose dimensions are given as-
Length = 5 cm, breadth = 3 cm and height = 2cm
12. Find the volume of a cube of edge 4 cm.
13. Find the volume of a cuboid whose dimensions are given as
Length = 10 cm , breadth = 5 cm and height = 3cm
14. Find the volume of a cube of edge 6 cm.
15. Find the volume of a cuboid whose dimensions are given as
Length = 15 cm , breadth = 8 cm and height = 5 cm
16. Find the volume of a cube of edge 10 cm.
17. Find the volume of a cuboid whose dimensions are given as
Length = 17 cm , breadth = 14 cm and height = 12cm
47. 18. Find the volume of a cuboid whose dimensions are given as
Length = 30 cm , breadth = 25 cm and height =18cm
19. Find the volume of a cube of edge 13 cm.
20. Find the volume of a cubical box of edge 15 cm.
21. Find the volume of a box of length 9 cm, breadth 5 cm and height 3 cm.
22. A dice has an edge of 4 cm. Find the volume of the dice.
23. An encyclopedia has a length 30 cm, breadth 20 cm and height 8 cm. Find the volume of the
encyclopedia.
24. Find the volume of a cubical box of edge is 8 cm.
25. Find the volume of a brick of length of 18 cm, breadth 9 cm and height 6 cm.
26. Each side of a cubical gift box is 11 cm. Find its volume.
27. The length, breadth and height of a cuboidal room is 12 m, 8 m and 4 m respectively. Find
the volume of the room ?
28. The length, breadth and height of cubical vessel are 10 m, 8 m and 5 m respectively . Find
the volume of the liquid that the vessel can hold.
29. Which has more volume? A cuboid of length 7cm, breadth 5 cm and height 4 cm or a cube of
edge 6cm.
30. Which has more volume and by how much? A cuboidal box of length 8cm, breadth 7 cm and
height 5 cm or a cubical box of edge 5 cm.
48. SUB-MATHEMATICS, CLASS-IV, CHAPTER-VOLUME,
WORKSHEET( STANDARD)
Choose the correct answer.
1. The measure of space a solid occupies is called its-
(i) volume (ii) area (iii) perimeter (iv) none of these
2. Which of the following has the least volume?
(i) football (ii) cricket ball (iii) table tennis ball (iv) golf ball
3. Which of the following units is not used to measure volume?
(i) cu. mm. (ii) cu. cm. (iii) cu. m. (iv) sq. m.
4. Cube is the best unit for measuring-
(i) Area (ii) volume (iii) perimeter (iv) length
5. volume of a cube of edge 1 mm is-
(i) 1mm (ii) 1 sq.mm (iii) 1 cu.mm (iv) 3 mm
Fill in the blanks.
6. ____________ of a solid depends on the outer physical size.
7. Volume of a cube = __________ × ____________ × Edge .
49. 8. Volume of a cuboid = __________ × ____________ × Height
9. Volume of a cube of edge 1 cm is_____________.
10. If a box is filled with 18 cubes of edge 1 cm each, its volume is ____________.
Answer the following questions.
11. Find the volume of a cuboid whose dimensions are given below.
Length = 30 cm , breadth = 24 cm and height = 15 cm
12. Find the volume of a cube of edge 17 cm.
13. Find the volume of a brick of length 24 cm, breadth 12 cm and height 8 cm.
14. A cuboidal water tank is 6 metre long, 5 metre wide and 4 metre deep. Find the volume of the tank.
15. Two cubes each with side 8 cm joined to form a cuboid . What is the volume of the cuboid so
formed?
16. An aquarium is the form of a cuboid whose length is 80 cm, breadth is 30 cm and height is 40 cm.
Find the volume of the aquarium?
17. A cubidal wooden box is 95 cm long, 72 cm wide and 64 cm high . Find the volume of the box.
18. A godown is in the form of a cuboid of length 60 m, breadth 40 m and height 30 m . Find the
volume of the grains that can be stored in the godown.
19. Which has more volume? A cuboidal vessel of length 17cm, breadth 15 cm
and height 12 cm or a cubical vessel of edge 14 cm.
20. A child playing with building blocks, which are of the shape of cubes, has
build a structure as shown in the figure. If the edge of each cube is 3 cm, find
the volume of the structure built by the child .
50. SUB-MATHEMATICS, CLASS-IV, CHAPTER-VOLUME,
WORKSHEET( ADVANCED)
1. The length of a cuboid is 15 cm, breadth is 10 cm and height is 2cm less than breadth. Find the
volume of the cuboid.
2. A cubical box of edge 12 cm is one-fourth filled with salt. Find the volume of salt in the box.
3. The edge of a cubical box is 6 cm. Half of the box is filled with sand. Find the volume of the sand.
4. A cube has an edge of 8 cm. If each edge of the cube is doubled find the volume of the new cube.
5. A cuboidal box of dimensions 60 cm × 50 cm × 30 cm. How many small cubes with side 1 cm can
be placed in the box ?
6. A match box has a length of 4 cm, breadth 3 cm and height 2 cm. What will be the volume of a
packet containing 12 such match boxes ?
7. Two cubes each with side 14 cm joined to form a cuboid . What is the volume of the cuboid ?
8. A solid cube of an edge 12 cm is cut in to 8 cubes of equal volume. What will be the volume of each
cube?
9. A godown is in the form of a cuboid of volume 72,000 cu.m . If the length and breadth of the floor
of the godown is 60 m and 40 m respectively, find its height.
10. The length, breadth and height of a cuboidal water tank are 15 m, 12 m and 8 m respectively. If
half of the tank is filled with water, find the volume of water in the tank.
