1. Whiteboardmaths.com
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2. Intro Density/Mass/Volume Aluminium Copper Gold
Three identical shaped blocks of metal have a volume of 48 cm3.
Use the scales to calculate the mass of 1 cm3 of each metal.
The mass of 1 unit (cm3 or m3) of a substance is called its density (d).
d = 2.7g/cm3
d = 8.9g/cm3
d = 19.3g/cm3
926
130
900
100
900
100
900
100
800
200
800
200
800
200
700
300
700
300
700
300
grams
grams
grams
600
400
600
400
600
400
500
500
500
427
Intro
Aluminium
Copper
Gold
1 cm3 =
130 48
= 2.7g
1 cm3 =
427 48
= 8.9g
1 cm3 =
926 48
= 19.3g

3. Remember that 1 m3 = 100 cm x 100 cm x 100 cm
So to convert from g/cm3 to kg/m3 we need to multiply by
100 cm
4.6 g/cm3 
4600 kg/m3
1 m3
100 cm
The SI Unit of density is kg/m3 and these units are frequently used by engineers.
Cubic metre
1 cm3
Not to scale
100 cm

4. or equivalently:
d = kg/m3
d = kg/m3
d = kg/m3

5. So density =
mass
volume
volume =
mass
density
mass = density x volume

6. Symbolically:
d = m v
v = m d  
m = dv

7. Problems d = m v v = d m = dv d = m v 204 d = 600 = 0.34 g/cm3
Density/Mass/Volume
d = m v
v = d
m = dv
v = 600 cm3
m = 204 g
1. A block of cork has a volume of 600 cm3 and a mass of 204g. Find its density.
d = m v
204
d =
600
= 0.34 g/cm3
Problems

8. Density/Mass/Volume
d = m v
v = d
m = dv
m = 7.36 g
2 cm
2. A cube of ice of side 2 cm has a mass of 7.36 g Find the density of ice.
d = m v
7.36
d = 8
= 0.92 g/cm3

9. m d = v 48 g 96 g v = d m = dv 75 g Density/Mass/VolumeB
d = m v
v = d
m = dv
48 g
4 cm
96 g
3 cm
4 cm
2 cm
4 cm
2 cm C
75 g
3 cm
1 cm
10 cm
3. Put the stones on order of density (Highest to Lowest).

10. d = m v v = d m = dv 48 g 96 g 75 g d = =2 g/cm3 d = =3 g/cm3 d =
Density/Mass/Volume A B
d = m v
v = d
m = dv
48 g
4 cm
96 g
3 cm
4 cm
2 cm
4 cm
2 cm C
75 g
3 cm B C A
The order is
1 cm
10 cm 96
d = 48
=2 g/cm3 48
d = 16
=3 g/cm3 75
d = 30
=2.5 g/cm3 A B C

11. 11 775 kg m d = v v = d m = dv m 11 775 d = = 7 850 kg/m3 d = v 1.5
Density/Mass/Volume
d = m v
v = d
m = dv kg
1 m
0.75 m
2 m
4. The block of industrial steel shown above was made at the Scunthorpe steelworks. What is the density of steel?
d = m v
11 775
d =
1.5
= kg/m3

12. A B C Rewrite these 3 densities in kg/m3 2000 kg/m3 3000 kg/m3

13. Cubic cm m d = v v = d m = dv Density/Mass/Volume
Did you know that 1 cm3 of water has a mass of 1 g?
d = m v
v = d
m = dv
1 cm
1 cm
1 cm
So the density of water is 1g/cm3
1 cm3 of water is also called a millilitre (ml).
Cubic cm

14. 5. Find the mass of water contained in the bottle.
Density/Mass/Volume
d = m v
v = d
m = dv
1 cm3
1 Litre
Did you know that 1 cm3 of water has a mass of 1 g?
5. Find the mass of water contained in the bottle.
m = d x v
= 1 x 1000 = 1000g = 1 kg

15. Find its mass (nearest kg)
Density/Mass/Volume
d = m v
v = d
m = dv
6. The head above is made of bronze (density 8.5 g/cm3). Its volume is 588 cm3.
Find its mass (nearest kg)
m = d x v
= 8.5 x 588 = 4998 g
= 5 kg (nearest kg)

16. Density/Mass/Volume
d = m v
v = d
m = dv
7. This miniature marble statue has a density of 2.65 g/cm3and a mass of 477 g. Find its volume.
v = m d
477
v =
2.65
= 180 cm3

17. Density/Mass/Volume
d = m v
v = d
m = dv
8. A tyre made of rubber (density 1.2 g/cm3) has a mass of 3.6 kg. Find its volume.
v = m d
3600
v =
1.2
= 3000 cm3

18. Worksheet Density/Mass/Volume Density (g/cm3) Mass (g) Volume (cm3)
Complete the table below. (answers to 1 dp where appropriate)
Density (g/cm3)
Mass
(g)
Volume
(cm3)
Mercury
13.6
3000
Iron
750
96.2
Lead
11.3
159.3
Gold
19.3 85
Aluminium
2.7
55.6
Copper
8.9
275
Marble
12350
4750
Teak
5000
7692
Concrete
2.3
15250
Worksheet

19. Density/Mass/Volume Density (g/cm3) Mass (g) Volume (cm3) Mercury 13.6
worksheet
Complete the table below. (answers to 1 dp where appropriate)
Density (g/cm3)
Mass
(g)
Volume
(cm3)
Mercury
13.6
3000
220.6
Iron
7.8
750
96.2
Lead
11.3
1800
159.3
Gold
19.3 85
4.4
Aluminium
2.7
150
55.6
Copper
8.9
275
30.9
Marble
2.6
12350
4750
Teak
0.65
5000
7692
Concrete
2.3
15250
6630