The document provides an overview of measurement concepts in physics, focusing on volume, area, density, and speed. It includes definitions, units of measurement, key formulas, and example problems to illustrate calculations related to these concepts. Homework questions are also provided for students to reinforce their understanding.

1. WELCOME TO MY CLASS
Mr. Souvik Chatterjee
M.Sc (Physics)&B.Ed

2. PHYSICAL QUANTITY &
MEASUREMENT
Measurement of volume(3D Concept) Concept Of
unit volume
Measurement of area: Estimate the area of
irregular shape objects using graph paper
Measuirement of density of regular solids: Basic
concepts, Formula, Simple Numericals (S.I unit
not required
Calculation of speed: Basic Concept, Formula,
Simple Numericals (S.I unit not required)

3. KEY POINTS
 Measurement is a process of comparision of the given unknown
quantity with a fixed known quantity of the second kind called unit
 Magnitude= Number of times the unit is contained in the quantity X
Unit
 Length is the distance between two points. Its S.I unit is metre (m).
It is measured with the help of a metre rule or measuring tape.
 Mass is the quantity of matter contained in the body. Its S.I unit is
kilogram (kg). It is measured by a beam balance or an electronic
balance.
 Time is the interval of occurrence of an event. Its S.I unit is second
(s). It is measured with the help of a pendulum clock or a stop watch
or stop-clock
 Temperature is a quantity which measures the hotness and coldness
of a body. Its S.I unit is kelvin (K). It is measured using a
thermometer.

4. MEASUREMENT OF VOLUME
 The space occupied by an object is called volume
 S.I unit of volume is cubic metre (m3)
 Cubic metre is the volume of a cube with each side 1 meter
long
 1 m3 = 1m X 1m X 1m
 Cubic centimetre is the volume of cube with each side 1
centimeter
 1 cm3 = 1 cm X 1 cm X 1 cm
 1 m3 = 1 m X 1 m X 1 m = 100 cm X 100 cm X 100 cm
=1000000 cm3 = 10 6 cm3
 The volume of a liquids is generally expressed in litre (L)
 1 litre = 1000 cm3
 1 cm3 = 1 mL


5. VESSELS FOR MEASURING THE VOLUME OF
LIQUIDS
 Measuring Cylinder

6. Measuring Beaker

7. IMPORTANT FORMULA
Volume of Cube=(One side)3
Volume of Cuboid= Length X Breadth X Height
Volume of a sphere =4/3 X ∏ X (radius)3
Volume of a cylinder=∏ X (radius)2 X Height
 Volume of a Cone = ∏/3 X (radius)2 X Height
Where ∏=3.141 or 22/7

8. NUMERICAL PROBLEM
Problem-1. A box of dimensions 1.5 cm X 2.0
cm X 90.0 cm. Find the volume of the box in
(i) m3 (ii) cm3
(i) Volume= (1.5 X 2.0 X 90.0)= 270 cm3
1 cm3 = 1/1000000 m3
(ii) 270 cm3 = 270/1000000=0.00027 m3

9. Problem-2. A cylinder has length 80 cm and
radius 2 m. Find vo lume in (i) m3 (ii) cm3
Ans. (i) length= 80 cm= 80/100= 0.8 m
Volume= ∏ X 2 X 2 X 0.8 = 10.05 m3
 1 m3 = 100000 cm3
(ii)10.05 m3 = 10.05 X 1000000 cm3 = 10050000
cm3

10. Problem 3-A measuring cylinder contains
water to a level 0f 20 mL. The water level rises
to 50 mL. When a piece of copper is
completely immersed in it. Find the volume of
copper piece in (i) cm3 (ii) m3
Ans.(i) Volume= (50 − 20) mL = 30 mL = 30
cm3
 (ii) 30 cm3 = 20/1000000 m3 = 0.00003 m3

11. HOME WORK
1. What is measurement?
2. What is unit?
3. How is the magnitude of a quantity expressed?
4. Define and state the unit of the following:
(a)Length
(b)Mass
(c)Time
(d)Temperature

12.  5. Define volume. State its S.I unit.
 6. Define S.I unit of volume.
 7. Define 1 cubic cm. Establish the relation between
cubic meter and cubic centimeter.
 8. State the unit by which volume of liquid is
expressed? State its relation with cubic centimeter
 9. State the instruments by which volume of liquid can
be expressed.
 10. State the formulas:
 (a) Volume of a cube
 (b) Volume of a cuboid
 (c) Volume of a sphere
 (d) Volume of a cylinder
 (e) Volume of a cone

13. MEASUREMENT OF AREA
 The surface occupied by an object is called its area.
 S.I unit of area is square metre (m2)
 1 m2 is the area of a square of side 1m
 Bigger units of area are square decametre (or are) ,hectare and square
kilometre.
 One are is the area of a square with each side measuring 10 m. 1 are = 100
m2
 One hectare is the area of a square with each side measuring 100 m. 1
hectare = 10000 m2 = 100 are
 One kilometre square (km2) is the area of a square of each side measuring
1 km. 1 km2 = 1000000 m2
 To express area of small objects like pencil, rubber etc square metre is a big
unit. The smaller units of area are square centimetre(cm2) or square
millimetre (mm2).
 1 cm2 = 1/10000 m2
 1 mm2 = 1/1000000 m2

14. FORMULA
Area of a sphere= (one side)2
Area of a rectangle= Length X Breadth
Area of a circle= ∏ X (radius)2
Surface Area of a cylinder = 2∏ X (radius) X
length
Surface area of a sphere = 4∏ X (radius)2

15. NUMERICAL PROBLEM
Numerical-4 The diameter of a circular park is
140 cm. Find the surface area in (i) cm2 (ii) m2
 Radius= 140/2= 70 cm
(i)Area= ∏ X (radius)2 = (22/7 X 70X70)cm2
=(22 X 10X70)=15400 cm2
(ii)=15400/10000=1.54 m2

16. Numerical-5 Find the area of a cylinder of
radius 1m and length 210 cm. Find the area in
(i) cm2 (ii) m2
Length= 210 cm= 2.1 m
Area= ∏ X 1 X1 X 2.1= (22/7 X 2.1) =(22
X 0.3)=6.6 m2
6.6 m2 = 6.6 X10000 = 66000 cm2

17. DENSITY
 Density of a substance is defined as the mass of a unit
volume of that substance.
 S.I unit of density kilogram/metre3 (kg/ m3 )
 C.G.S unit of density gram/centimetre3(g/cm3)
 1 g/cm3=1000 kg/ m3
 1 kg/m3 = 1kg/ 1m3 =1000g/(100)3 cm3 =
1g/1000 cm3 = 1/1000 g/cm3
1 g/cm3 = 1000 kg/m3
 Density of copper is 8.9 g/cm3 means ‘The
mass of of copper having volume 1cm3 is 8.9
gram’

18. NUMERICAL PROBLEM
Numerical-6 Refer to the problem-3. If the
mass the substance is 234 g. Find the density
in (i) g cm-3 (ii) kg m-3. Identify the substance.
From the numerical- 3 volume = 30 ml= 30
cm3
Density= 234/30= 7.8 g cm-3 = 7.8 X 1000 =
7800 kg m-3
The substance is iron

19. Numerical-7 The mass of a wooden
block is 86 g. If the density of wood
is 800 kg m-3. Find the volume of
block.
Density = 800 kg m-3 = 800/1000 g
cm-3 = 0.8 g cm-3
 Volume = 86/0.8 = 107.5 cm3

20. SPEED
The distance travelled by the body in unit time
is called speed of the body.
S.I unit of speed is metre/second(m/s)
Some times we measure speed in kilometre/
hour(km/h)
1 m/s= 3.6 km/h or 5 m/s=18 km/h
Speedometre of a vehicle such as scooter, car
shows the speed of the the vehicle at that
instant.

21. 1 km/h= 1 km/ 1 hour =
1000 m/3600 s = 1000/3600 X 1m/1s = 5/18
X 1m/s
18 km/h = 5 m/s
Numerical-8 Convert the following speeds in
m/s (a) 5 km/min (b) 54 km/h
(a) 6 km/min = 6000 m/60 s = 6000/60 X
1m/1s= 100 X 1 m/s = 100 m/s
(b) 54 km/h = 54 X 5/18 = 15 m/s

22. Numerical-9 A cyclist is moving with a
speed of 30 km/h. How long will he take
to travel a distance of 900 m?
Distance = 900 m = 900/1000 = 0.9 km
Time = distance/ speed = 0.9/30 = 0.03 h
= 0.03 X 3600 s = 108 s.

23. HOME WORK
Define area. State and define its S.I unit.
Define: (a) one are (b) one hectare (c) one
square kilometer. How is each of them related to
S.I unit of area.
 State the formula:
 (a) Area of a square
 (b) Area of a rectangle
 (c) Area of a circle
 (d) Surface area of a cylinder
 (e) Surface area of a sphere.

24.  Define density. State its S.I unit.
 State the use of barometer?
Define speed. State its S.I unit.
Establish the relation between meter per
second and kilometer per hour.

25. NUMERICALS FROM CONCISE
PHYSICS
1.The length, breadth and height of a water
tank are 5m, 2.5m and 1.25m respectively.
Calculate the capacity of the water tank in (a)
cm3 (b) litre
 (a) Capacity of the water tank= volume of the
water tank = (5 X 2.5 X 1.25) = 15.625 m3
(b) 1 m3 = 1000 litre
15.625 m3 = 15.625 X 1000 = 15625 litre

26. 2.A solid silver piece is immersed in water
contained in a measuring cylinder. The level of
water rises from 50 ml to 62 ml. Find the volume
of silver piece.
Ans. Volume of the silver piece = (62 − 50) [1 ml
= 1 cm3 ] = 12 ml = 12 cm3
3.Find the volume of a liquid present in a dish of
dimensions 10 cm X 10 cm X 5 cm.
Ans. Volume of liquid = Volume of dish =
(10 X 10 X 5) = 500 cm3

27. 4.A rectangular field is of length 60 m and
breadth 35 m. Find the area of the field.
Ans. Area of the rectangle = (60 X 35)
= 2100 m2
6. A piece of brass of volume 30 cm3 has a
mass of 252 g. Find the density of brass in (i)
g/cm3 (ii) kg/m3
 Ans (i) Density = 252/30 = 8.4 g/cm3
(ii) 8.4 X 1000 = 8400 kg/m3

28.  7.The mass of an iron ball is 312g. The density of iron
is 7.8 g/cm3 . Find the volume of the ball.
 Ans. Volume of the ball = 312/7.8 = 40 cm3
 8. A cork has volume 25 cm3. The density of the cork
0.25 g/cm3. Find the mass of the cork.
 Ans. Mass of the cork = (25 X 0.25) = 6.25 g.
 9. Mass of 5 litre of water is 5 kg. Find the density of in
g/cm3.
 Volume = 5 L = 5000 ml = 5000 cm3
 [1 ml = 1 cm3 ]
 Mass = 5 kg = 5000 g
 Density = 5000/5000 = 1 g/cm3

29. 10. A cubical tank of side 1 m is filled with 800
kg of a liquid. Find: (i) The volume of the tank,
(ii) the density of the liquid in kg/m3
Ans.(i) Volume= (1)3 m3 = 1 m3
(ii)Density = 800/1 = 800 kg/m3
11.A block of iron has dimensions 2m X 0.5m X
0.25m. The density of iron is 7.8 g/cm3. Find the
mass of the block.
Ans. Volume = (2 X 0.5 X 0.25) = 0.25 m3
 Density = 7.8 X 1000 = 7800 kg/m3
Mass = 7800 X 0.25 = 1950 kg

30. 12.The mass of a lead piece is 115 g. When it
is immersed into a measuring cylinder, the
water level rises from 20 ml mark to 30 ml
mark. Find:
(i) The volume of the lead piece
(ii) The density of the lead in kg/m3
Ans. (i) Volume of the lead piece = (30 −
20) ml = 10 ml = 10 cm3
 (ii) Density = 115/10 = 11.5 g/cm3 = (11.5 X
1000) = 11500 kg/m3

31. 13. The density of copper is 8.9 g/cm3. What
will be its density in kg/m3?
Ans.8.9 g/cm3 = 8.9 X 1000 = 8900 kg/m3.
14. A car travels a distance of 15 km in 20
minutes. Find speed of the car in (i) km/h (ii)
m/s.
Ans.(i) Time = 20 minutes = 20/60
= 1/3 hour
Speed of car = 15/ (1/3) = 15 X 3= 45 km/h
(ii) 45 km/h = 45 X (5/18) = 12.5 m/s

32. 15.How long a train will take to travel a distance
of 200 km with a speed of 60 km/h?
Ans. Time = 200/60 = 10/3 hour =
(10/3 X 60) minute = 200 minutes = 3 h
20 mins
16. A boy travels with a speed of 10 m/s for 30
minute. How much distance does he travel?
Ans. Time = 30 minute = (30 X 60) = 1800 s
Distance = (10 X 1800) = 18000 m = 18 km.

33. 17.Express 36 km/h in m/s.
Ans. 36 km/h = 36 X (5/18) m/s
= 2 x 5 m/s = 10 m/s
18. Express 15 m/s in km/h.
Ans. 15 m/s = 15 X (18/5) = 3 X 18
km/h = 54 km/h

34. IMPORTANT QUESTIONS
How does density of water changes when
(a)It is heated from 0 degree C to 4 degree C
(b) It is heated from 4 degree C to 10 degree C
Ans. (i) Increase Because of ANOMOLOUS
Expansion Of WATER
(ii) Decrease

35. A car travels with a speed 12 m/s, while a
scooter travels with a speed 36 km/h, which of
the two travels faster?
Ans 36 km/h = (36 X 5/18) m/s
= (2 X 5) m/s = 10 m/s
Which is less than speed of car.
So the car travels faster

36. THANK
YOU