What is Volume?
The space occupied by any object is called the volume.
- Volume is three dimensional.
- To measure the volumes we need to know the measure of 3 sides.
- Since, volume involve involves 3 sides, so it is measured in cubic units.
What is meant by Plane Surface?
- Surface like the page of a book, blackboard, etc. are called plane surfaces.
- They do not have any volume but have only area.
Cube
A cube is a solid box whose each surface is a square of same area.
Therefore, cube has:
- 6 surfaces or faces,
- 8 vertices,
- 12 edges or sides of equal length.
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
Or
= length x length x length = l x l x l cu units
Or
= area x side cu units (And we know that area of square = side x side)
Cuboid
A cuboid is a solid box whose every surface is a rectangle of same area or different areas. A cuboid has length, breadth and height.
Therefore, cuboid has:
- 6 surfaces or faces,
- 8 vertices,
- 12 edges or sides
Volume of a cuboid
Cuboid is similar to rectangle.
So, Volume of a cuboid
= length x breadth x height = l x b x h cubic units
Or
= area of one surface x height cu units (as area =l x b)
Note:
= length x breadth x height = l x b x h cubic units
Or
= area of one surface x height cu units (as area =l x b)
Note:
In a cuboid, when the length, breadth and height are of different units, convert them to a same unit and solve.
How to find Volume by counting cubes?
Step: Find 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.Example:
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:
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
And 12 mm = 12/10 = 1.2 cm
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 cm
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.
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
And 12 mm = 12/10 = 1.2 cm
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 cm
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
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
Practice Exercise
Q1) Find the volume of a cube whose edge is 10 cm long.Q2) Find the volume of a cube of side 15 cm.
Q3) Calculate the volume of water that can be stored in a cubical tank whose each side measure 50 cm from inside.
Q4) Find the volume of a cube of side 10 cm in cubic meters.
Q5) Find the volume of a cuboid of dimensions 200 mm × 8 cm × 150 mm.
Q6) If the volume of a cuboid is 500 cu cm and the length is 100 cm and breadth is 50 cm, find the height.
Q7) Find the volume of oil that can be stored in a container of dimensions 15 cm × 10 cm × 11 cm.
Q8) Find the volume of a cuboid of dimensions 8000 mm × 900 cm × 12 m.
Q9) A tank is 45 m long, 25 m wide and 20 m high. Water is filled up to height of 100 cm. How much more water can it hold?
Q11) A cubical block of a metal was cut into 10 equal cubes of 5 cm. Calculate the volume of the block of metal?
Q12) A cuboid measures 27 cm x 18 cm x 9cm. How many cuboids of dimensions 9 cm x 3 cm x 1 cm can be cut from it?
Q13) Find the volume of a cuboid of dimensions 800 cm × 900 cm × 1 m.