Student calculation sheet P6

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Student calculation sheet P6 - Weebly

P6 1 Student calculation sheet Name Class Date

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P6.1

Student calculation sheet

Name ..................................................................... Class ................. Date ..................... © Oxford University Press 2016 www.oxfordsecondary.co.uk/acknowledgements

This resource sheet may have been changed from the original. 1

Density

Specification references: P3.1.1 Density of materials

M1a, M1b, M2a, M3b, M3c, M5c

Aims In this sheet, you will work through two worked examples designed to allow you to improve your maths skills. The focus is on solving algebraic equations, by substituting numbers into the equation and rearranging if needed. The algebraic equation is the formula for density. Learning outcomes After completing this activity, you should be able to: determine the volume of rectangular shapes convert between g and kg convert between litres, millilitres and cm 3 apply the relationship between density, mass, and volume substitute numerical values into algebraic equations using appropriate units solve algebraic equations. Worked examples

1 A student pours out 1 litre of a liquid and finds its mass is 0.7 kg. Calculate the

density of the liquid.

Step 1: Write down what you know

Volume 1 litre, Mass 0.7 kg, density ?

Step 2: Convert your units (either into g and cm3

or kg and m 3

Volume 1 litre 1000 ml (1 litre 1000 ml)

Volume 1000 cm3

(1 ml 1 cm 3

Mass 0.7 kg (1 kg 1000 g)

Step 3: Write the numbers into the equation and calculate

Density

(g/cm3 )mass (g) volume (cm 3 700

10000.7 g/cm

3 P6.1

Student calculation sheet

Name ..................................................................... Class ................. Date .....................

2 A block of wood has a density of 0.8 g/cm

3 . The block measures

30 cm 10 cm 10 cm. Calculate the mass of the block of wood in kg.

Step 1: Write down what you know

Density 0.8 g/cm

3 , length 30 cm, depth 10 cm, height 10 cm, mass ?

Step 2: Convert your units (either into g and cm

3 or kg and m 3 Not needed but you do need to find volume in this question.

Step 3: Calculate the volume

Volume 30 10 10 3000 cm

3 (volume length depth height)

Step 4: Write the numbers into the equation

Density

(g/cm 3 )mass (g) volume (cm 3

0.8mass

3000
This time the question wants you to calculate the mass. Mass is not the subject of the formula. Step 5: Rearrange the equation so that mass is the subject of the formula

Multiply both sides of the equation by 3000

0.8 × 3000 = mass

2400 g mass

Mass in kg 2.4 kg (1 kg 1000 g)

Questions

1 Convert the following to cm

3 a 100 ml (1) b 2 litres (1) P6.1

Student calculation sheet

Name ..................................................................... Class ................. Date .....................

2 A tennis ball has a volume of 150 cm

3 and mass of 58 g. Calculate the density of the tennis ball. State the units. (3)

3 An ice cube has the dimensions 3 cm 2 cm 2 cm. The mass of the ice

cube is 10.8 g. Calculate the density of ice. (3)

4 A miner finds a sample of rock and is convinced it contains gold. He looks up

the density of gold and discovers gold has a density of 19 g/cm 3 , whilst 'fool's gold' has a density of 5 g/cm 3 . The mass of his sample is 5.5 kg and the volume of water displaced by it is 300 cm 3 a Calculate the density of the sample in g/cm 3 (2) b Discuss whether you think the miner had found gold or fool's gold. Explain your answer. (2)

5 Molten iron has a density of 7.0 g/cm

3 . In its solid state, iron has a density of

8.0ௗg/cm

3 a Calculate the volume of 10 kg of molten iron. (3) b Calculate the volume of 10 kg of solid iron. (3) P6.1

Student calculation sheet

Name ..................................................................... Class ................. Date .....................

© Oxford University Press 2016 www.oxfordsecondary.co.uk/acknowledgements This resource sheet may have been changed from the original. 4 c Molten iron fills a mould, which has a volume of 200 cm 3 . Calculate the volume when the iron cools and solidifies. (2)

6 A fish tank with mass 1.0 kg is placed on a shelf. The dimensions

are 37 cm 15 cm 28 cm. The shelf can hold a mass of 16 kg and the density of the water inside it is 1.0 g/cm 3 a Calculate the maximum volume of water the fish tank can contain. (1) b Determine whether the shelf is strong enough for the fish tank when it is full of water. Explain your answer (3)

7 A hollow plastic ball has volume of 250 cm

3 and a mass of 150 g. To float, the ball must have a density less than 1.0 g/cm 3 a Calculate the density of the ball. (1) b The ball is floating in water, but it has a small hole and is slowly filling with water. Calculate how much water will flow into it before it sinks. (3) P6.1

Student calculation sheet

Name ..................................................................... Class ................. Date .....................

Answers

8 a 100 cm

3 (1) b 2000 cm 3 (1)

9 Density =

15058
)(cm volume(g) mass 3 (1) = 0.39 g/cm 3 (1 mark for answer, 1 for units)

10 Volume l d h 3 2 2 12 cm

3 (1)

Density

1210.8

)(cm volume(g) mass 3 (1) = 0.9ௗg/cm 3 (1)

11 a Density

3005500

)(cm volume(g) mass)(g/cm 33
(1) = 18ௗg/cm 3 (1) b Gold (1) The density of the rock is much closer to that of gold than that of fool's gold (accounting for the fact that the sample is not pure). (1)

12 a Density

(g/cm 3 )mass (g) volume (cm 3 so densitymassvolume (1)

Volume =

7.010000

(1) ௗ= 1400ௗg/cm 3 (to 2sf) (1429) (1) b Density (g/cm 3 )mass (g) volume (cm 3 so densitymassvolume (1)

8.010000Volume

(1) = 1300ௗg/cm 3 (to 2 sf) (1250) (1) c Mass of iron density volume 7.0 200 14 (1) (175)180cm8.01400 densitymassVolume 3 (1)

13 a Volume l d h 37 15 28 15ௗ540 = 16ௗ000 cm

3 (1) b Mass of water density volume 1 15ௗ540 15.54 kg (1) Total mass mass of water mass of fish tank 1.0 15.54 16.54 kg (1) The shelf is not strong enough as the total mass is greater than 16ௗkg. (1) P6.1

Student calculation sheet

Name ..................................................................... Class ................. Date .....................

14 a Density

150
250

0.6 g/cm

3 (1) b Mass density volume 1 250 (1 mark for rearrangement, 1 mark for realising have to set density 1)

Mass of water that can be added 250 - 150 (1)

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[PDF] Student calculation sheet P6 - Weebly

Student calculation sheet

Density

M1a, M1b, M2a, M3b, M3c, M5c

1 A student pours out 1 litre of a liquid and finds its mass is 0.7 kg. Calculate the

Step 1: Write down what you know

Volume 1 litre, Mass 0.7 kg, density ?

Step 2: Convert your units (either into g and cm3

Volume 1 litre 1000 ml (1 litre 1000 ml)

Volume 1000 cm3

Mass 0.7 kg (1 kg 1000 g)

Density

10000.7 g/cm

Student calculation sheet

2 A block of wood has a density of 0.8 g/cm

30 cm 10 cm 10 cm. Calculate the mass of the block of wood in kg.

Step 1: Write down what you know

Density 0.8 g/cm

Step 2: Convert your units (either into g and cm

Step 3: Calculate the volume

Volume 30 10 10 3000 cm

Step 4: Write the numbers into the equation

Density

0.8mass

Multiply both sides of the equation by 3000

0.8 × 3000 = mass

2400 g mass

Mass in kg 2.4 kg (1 kg 1000 g)

Questions

1 Convert the following to cm

Student calculation sheet

2 A tennis ball has a volume of 150 cm

3 An ice cube has the dimensions 3 cm 2 cm 2 cm. The mass of the ice

4 A miner finds a sample of rock and is convinced it contains gold. He looks up

5 Molten iron has a density of 7.0 g/cm

8.0ௗg/cm

Student calculation sheet

6 A fish tank with mass 1.0 kg is placed on a shelf. The dimensions

7 A hollow plastic ball has volume of 250 cm

Student calculation sheet

Answers

8 a 100 cm

9 Density =

10 Volume l d h 3 2 2 12 cm

Density

1210.8

11 a Density

3005500

12 a Density

Volume =

7.010000

8.010000Volume

13 a Volume l d h 37 15 28 15ௗ540 = 16ௗ000 cm

Student calculation sheet

14 a Density

0.6 g/cm

Mass of water that can be added 250 - 150 (1)