The space occupied by any object is called the volume.
is three dimensional. To measure the volumes we need to know the measure of 3
volume involves 3 sides, so it is measured in cubic units.
Surface like the page of a book, blackboard, etc. are called
plane surfaces. They do not have any volume but have only area.
is a solid box whose each surface is a square of same area.
Therefore, cube has:
6 surfaces or faces
12 edges or sides of equal length
Volume of a cube with side length 1 unit is 1 cubic
unit. Such cube is called a "unit cube," and used as unit of volume.
of a cube
A cube has all sides are of equal length,
So, Volume of a cube = side x side x side = S x
S X S cu units
= length x
length x length = l x l x l cu units
= area x side
cu units (And we know that area of square = side x side)
of a cuboid
cuboid is a solid box whose every surface is a rectangle of same area or
different areas. A cuboid has length, breadth and height.
So, Volume of a cuboid = length x breadth x
height = l x b x h cubic units
= area of one
surface x height cu units (as area =l x b)
In a cuboid, when the length, breadth and height are of different units,
convert them to a same unit and solve.
by counting cubes
out the number of unit cubes that form the solid or fill up the entire space
occupied by the given solid such as cuboid and cube.
Take an empty cube shaped box of edge 4 cm with open
top. Now fit cubes of edges 1 cm in it.
How many cubes of 1 cm can be fitted into
cube box of edge 4 cm?
From the observation, it is clear that 64 such cubes
will fit into it. So the volume of the box will be equal to
the volume of 64 unit cubes together.
Therefore, the volume of the cube = 64 cu cm
Note that 64 = 4 × 4 × 4
Illustration 1: Find
the volume of a cube of side 8 cm.
Solution: Volume of cube = l x l x l = 8 x 8 x
8 = 512 cu cm
Illustration 2: Find
the volume of a cuboid of dimensions 16 cm x 10 m x 6 cm.
Solution: Volume of cuboid = l x b x h = 16 x
10 x 6 = 960 cu cm
Illustration 3: Find
the volume of a cuboid of dimensions 18 cm x 30 mm x 15 cm.
Solution: l = 18 cm, b = 30 mm = 3 cm (10 mm =1
cm, 30/10 = 3 cm), h = 15 cm
Volume of cuboid = l x b x h = 18 x 3 x 15 = 810 cu cm
Illustration 4: Find
the volume of a cuboid of dimensions 21 mm x 2 cm x 12 mm in cu. cm.
Solution: 10 mm = 1 cm
Therefore, 21 mm = 21/10 cm = 2.1 cm, 12 mm = 12/10 =
Length = 2.1 cm, breadth = 2 cm, height = 1.2 cm
Volume of cuboid = l x b x h = 2.1 x 2 x 1.2 = 5.04 cu
Illustration 5: Find
the number of cubical boxes of cubical side 5 cm, which can be accommodated in
carton of dimensions 25 cm x 10 cm x 15 cm.
Solution: Volume of cubical box = side x side
x side = 5 x 5 x 5 = 125 cu cm
Volume of carton = 25 x 10 x 15 = 3750 cu cm
No. of boxes = Volume of carton/Volume of each box =
3750/125 = 30