The document defines density as mass per unit volume and provides the formulas for calculating density, mass, and volume given two of the quantities. It also defines relative density as the ratio of the mass of a substance to the mass of an equal volume of water. Some example calculations are provided to demonstrate how to use the formulas and concepts to calculate density, mass, volume, and relative density for different substances and scenarios.

1. DENSITY
 The density of a substance is its mass
per unit volume
 Density = Mass / Volume (kg/m3) or
(g/cm3)
 Mass = Density x Volume (kg) or (g)
 Volume = Mass / Density (m3) or (cm3)

2. FORMULAE
Distance = Speed x Time
If we want to find speed, divide each side
by time:
Distance = Speed x Time
Time Time
Distance = Speed
Time
Speed = Distance
Time

3. FORMULAE
Force = Mass x Acceleration
Find Mass.

4. FORMULAE
Force = Mass x Acceleration
If we want to find acceleration. Divide
each side by mass:
Force = Mass x Acceleration
Mass Mass
Force = Acceleration
Mass
Acceleration = Force
Mass

6. FORMULAE
Speed = Distance
Time
 If we want to find time. We cross multiply.
Speed = Distance
1 Time
 Distance = Speed x Time
Now we divide by speed.
Distance = Speed x Time
Speed Speed

7. FORMULAE
Distance = Speed x Time
Speed Speed
Distance = Time
Speed
Time = Distance
Speed

8. FORMULAE
Acceleration = Force
Mass
Find mass.

9. FORMULAE
Acceleration = Force
Mass
Find mass. We cross multiply.
Acceleration = Force
1 Mass
Force = Acceleration x Mass
Now we divide by acceleration.
Force = Acceleration x Mass
Acceleration Acceleration

10. FORMULAE
Now we divide by acceleration.
Force = Acceleration x Mass
Acceleration Acceleration
Force = Mass
Acceleration
Mass = Force
Acceleration

12. DENSITY
 The density of a substance is its mass
per unit volume
 Density = Mass / Volume (kg/m3) or
(g/cm3)
 Mass = Density x Volume (kg) or (g)
 Volume = Mass / Density (m3) or (cm3)

13. DENSITY
 The density of water is 1000 kg/m3 or
1g/cm3
 1 litre of water has a mass of 1 kilogram
(kg).
 1 cm3 of water has a mass of 1 g
 1 m3 of water has a mass of 1000 kg

14. RELATIVE DENSITY
 The relative density or specific gravity of
a substance is the ratio of the mass of
any volume of it to the mass of an equal
volume of water.
 Relative density =
mass of any volume of the
substance
mass of an equal volume of
water

15. RELATIVE DENSITY
 The relative density or specific gravity of
a substance is the ratio of the weight of
any volume of it to the weight of an equal
volume of water.
 Relative density =
weight of the substance
.
weight of an equal volume of
water

16. RELATIVE DENSITY
 The relative density or specific gravity of
a substance is the number of times the
substance is denser than water.
 Relative density = density of the
substance
density of water
 Relative density has no units

17. RELATIVE DENSITY
 The relative density of a substance is the
same number as its density in g/cm3.
 For example. The relative density of
brass is 8.5 and its density is 8.5 g/cm3

18. QUESTION 1
Calculate the density of water or prove
that the density of water is 1 g/cm3 and
1000 kg/m3
1 cm3 of water has a mass of 1 g.
Density = mass / volume = 1g /1 cm3
= 1 g/cm3

19. QUESTION 1
Calculate the density of water or prove
that the density of water is 1 g/cm3 and
1000 kg/m3
1 m3 of water has a mass of 1000 kg
Density = mass / volume
= 1000 kg /1m3 = 1000 kg/m3

20. QUESTION 2
What is the SI unit for density?

21. QUESTION 2
What is the SI unit for density?
kg/m3

22. QUESTION 3
What is the mass of 50 cm3 of water?
1 cm3 of water has a mass of 1 g.
50 cm3 of water has a mass of:
50 x 1 g = 50 g

23. QUESTION 4
What is the mass of 100 ml (millilitres) of
water?
1 litre of water has a mass of 1 kg.
1 litre of water = 1000 ml
1000 ml of water = 1 kg
1 ml of water is 1/1000 kg.
100 ml = 100 x 1/1000 = 0.1 kg or 100 g

24. QUESTION 4
What is the mass of 100 ml (millilitres) of
water?
1 m3 of water is = 1000 litres = 1000000 ml
1 m3 of water is = 1000000 cm3 = 1000000 ml
1 cm3 of water = 1000000 /1000000 = 1 ml
1 cm3 of water = 1 ml = 1 g
1 ml of water = 1 g
100 ml of water 100 x 1 = 100 g

25. QUESTION 4
What is the mass of 100 ml (millilitres) of
water?
1 cm3 of water = 1 ml = 1g
100 ml of water = 100 x 1 g = 100 g

26. QUESTION 5
Calculate the density of 5 cm3 of copper if
it has a mass of 44.5 g.
Density = mass / volume
= 44.5 g /5 cm3 = 8.9 g/cm3

27. QUESTION 6
Calculate the density of 1.5 m3 of lead if it
has a mass of 16,950 kg.
Density = mass / volume
= 16,950 kg /1.5 m3
= 11,300 kg/m3

28. QUESTION 7
A sheet of tinfoil measures 20 cm x 10 cm
x 0.1 mm. The density of the foil is 4
g/cm3. What is the mass of the tinfoil?
Volume of tinfoil = 20 x 10 x 0.01 = 2 cm3
Density = Mass / Volume
Mass of tinfoil = density x volume
= 4 g/cm3 x 2 cm3 = 8 g

29. QUESTION 8
The density of mercury is 13.5 g/cm3.
Find the volume of 1 kg of mercury.
Density = Mass / Volume
Volume = mass / density = 1 kg /13,500
kg/m3
= 0.00007407 m3

30. QUESTION 8
The density of mercury is 13.5 g/cm3.
Find the volume of 1 kg of mercury.
Density = Mass / Volume
Volume = mass / density
= 1000 g /13.5 g/cm3
= 74.07 cm3

31. QUESTION 9
The volume of the solution was measured
in a graduated cylinder was 45 cm3, if the
mass of solution measured to be 60.75
grams. What is the relative density of the
solution?
Relative density
= mass of any volume of the substance
mass of an equal volume of water
= 60.75 g = 1.35

32. QUESTION 10
An empty 60 litre petrol tank has a mass of 10 kg. What
will be its mass when full of fuel of relative density 0.72.
Relative density = mass of any volume of the
substance
mass of an equal volume of water
Mass of fuel = relative density x mass of an equal
volume of water
= 0.72 x 60 kg = 43.2 kg
Mass of tank when fill with fuel = mass of fuel + mass
of tank = 43.2 + 10 = 53.2 kg

34. QUESTION 12
A pump discharges 2000 litres of water
per minute at 6 bar pressure.
i) Calculate the water power of the pump.
Water power = 100 × L × P
60
= 100 × 2000 × 6
60
= 1,200,000
60
= 20,000 watts

35. QUESTION 12
If the pump is 70% efficient, calculate the
brake power of the engine driving the
pump.
Brake power = Water power (WP)
Efficiency
= 20,000 × 100
70
= 2,000,000
70
= 28571.43 watts

36. QUESTION 12
 If the design of the pump were to be improved
so that the discharge increased to 2400 litres of
water per minute at 6 bar, calculate the new
efficiency of the pump.
Water power = 100 × L × P
60
= 100 × 2400 × 6
60
= 1,440,000 = 24,000 watts
60

37. QUESTION 12
 If the design of the pump were to be improved
so that the discharge increased to 2400 litres of
water per minute at 6 bar, calculate the new
efficiency of the pump.
Water power = 24,000 watts
Efficiency = WP x 100
BP
= 24,000 × 100
28571.43
= 84 %