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Whiteboardmaths.com © 2007 All rights reserved 5 7 2 1

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

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 1 000 100 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

or equivalently: d = 2 700 kg/m3 d = 8 900 kg/m3 d = 19 300 kg/m3

So density = mass volume volume = mass density mass = density x volume

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

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

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

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

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

11 775 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 11 775 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 = 7 850 kg/m3

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

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

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

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)

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

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

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

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