DENSITY[ESTIMATED TIME: 75 minutes] GCSE

(+ IGCSE) EXAM QUESTION PRACTICE

-1-

1. The mass of 4 m3 of copper is 35 800 kg. Calculate the density of the copper. .............................. kg/m3

(2)

2. The density of steel is 8050 kg/m3. Work out the mass of 5 m3 of steel. .................................... kg

(2)

3. A gold chain has a volume of 4 cm3. The density of gold is 19.3 grams per cm3. Calculate the mass of the gold chain. ...................................... g

(2)

1. [2 marks]

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Feb by Maths4Everyone.com, Extra Q1: 2 Marks

-1-

1. The mass of 4 m3 of copper is 35 800 kg. Calculate the density of the copper. .............................. kg/m3

(2)

2. The density of steel is 8050 kg/m3. Work out the mass of 5 m3 of steel. .................................... kg

(2)

3. A gold chain has a volume of 4 cm3. The density of gold is 19.3 grams per cm3. Calculate the mass of the gold chain. ...................................... g

(2)

2. [2 marks]

Note that these questions are sorted in date order (most recent questions first).

Feb by Maths4Everyone.com, Extra Q2: 2 Marks

-1-

1. The mass of 4 m3 of copper is 35 800 kg. Calculate the density of the copper. .............................. kg/m3

(2)

2. The density of steel is 8050 kg/m3. Work out the mass of 5 m3 of steel. .................................... kg

(2)

3. A gold chain has a volume of 4 cm3. The density of gold is 19.3 grams per cm3. Calculate the mass of the gold chain. ...................................... g

(2)

3. [2 marks]

Note that these questions are sorted in date order (most recent questions first).

Feb by Maths4Everyone.com, Extra Q3: 2 Marks

Questions compiled by:@Maths4Everyone

Contains questions which have been reproduced with the kindpermission of Pearson Education Limited UK

D I 35800V T 8950

8950

M VolxDen5 8050

40250

40250

Mass Vol x Density

4 X 19.3

77 2

77.2

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4. The mass of a standard gold bar is 1000 grams. The density of gold is 19.3 grams per cm3. Work out the volume of a standard gold bar. .................................. cm3

(2)

5. The density of concrete is 2.4 g/cm3. Work out the mass of a concrete slab which has a volume of 12 m3. Give your answer in kilograms. .................................... kg

(2)

4. [2 marks]

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Feb by Maths4Everyone.com, Extra Q4: 2 Marks

-3-

6.

Diagram NOT accurately drawn

The diagram shows a solid wooden block in the shape of a cuboid. The block is made from wood with density 0.58 g/cm3 Work out the mass of the block. ..................................................... g

(3)

4 cm

7 cm

2 cm 8 cm

3 cm

5 cm

4 m

5 m

3 m

5 cm

12 cm

8 cm

5. [3 marks]

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Feb by Maths4Everyone.com, Extra Q6: 3 Marks

Vol 1001 51.819.3

51.8

Mass Vol x Density

7 4 2 0.58

32.4832.5 to 3 S.f

32.5

-2-

4. The mass of a standard gold bar is 1000 grams. The density of gold is 19.3 grams per cm3. Work out the volume of a standard gold bar. .................................. cm3

(2)

5. The density of concrete is 2.4 g/cm3. Work out the mass of a concrete slab which has a volume of 12 m3. Give your answer in kilograms. .................................... kg

(2)

6. [2 marks]

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Feb by Maths4Everyone.com, Extra Q5: 2 Marks

-5-

4. The diagram shows a solid triangular prism.

Diagram NOT accurately drawn

The prism is made from steel. The density of the steel is 7.9 grams per cm3. Calculate the mass of the prism. Give your answer in kilograms, correct to 3 significant figures. ........................................................

(3) 5. One sheet of A4 paper has dimensions 21.0 cm by 29.7 cm. The paper has a mass of 80 g per m2.

Work out the total mass of 500 sheets of A4 paper. Give your answer in kilograms, correct to 3 significant figures.

8 cm

6 cm 11 cm

11 cm

5 cm 12 cm

13 cm

6 cm

5 cm

9 cm 4 cm

14 cm

9 cm 13 cm

12 cm

7. [3 marks]

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Feb by Maths4Everyone.com, Extra Q9: 3 Marks

Density 2.4 glen2.4 106 g m

2.4 103 Kg m3

Mass Vol Density12 2 4 10 28,800kg

28,800

Vol Ex 8 6 11 264cm

Mass Vol x Density264 X 7.9 2085.6g

2.0856 Kg2.09 Kg to 3 S f

2 09 kg

-7-

8. The diagram shows a solid rubber ball in the shape of a sphere.

Diagram NOT accurately drawn

The radius of the ball is 5 cm. The mass of the ball is 550 grams. An object will only float in water if its density is less than 1.0 g/cm3. Will this rubber ball float in water? You must show clear calculations to justify your answer. ........................................................

(4)

5 cm

16 cm

4 cm

0.3 cm

8. [4 marks]

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Feb by Maths4Everyone.com, Extra Q12: 4 Marks

Vol T550

Density Madq

1.0504 g cmVol

Ball sinks in water ie does not floatsince 1.05 1.00 g cm3

-8-

9. The diagram shows a steel girder in the shape of a prism.

Diagram NOT accurately drawn

The length of the girder is 180 cm. The cross sectional area of the girder is 18 cm2. The steel has a density 7.8 g/cm3. Justin has a pickup truck. The maximum load that Justin’s truck can carry is 500 kg. Find the maximum number of these steel girders that Justin can carry in his truck, without exceeding the maximum load. ........................................................

(5)

180 cm

9. [5 marks]

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Feb by Maths4Everyone.com, Extra Q13: 5 Marks

Mass of one girderVol x Den18 180 7.8 g25272g

25.272 Kg500

19.7825.272

Can carry 19 girders

-9-

10. 200g of aluminium and 200g of copper are mixed to make 400g of an alloy. Aluminium has a density of 2.7 g/cm3. Copper has a density of 8.9 g/cm3. Work out the density of the alloy. .............................................. g/cm3

(4)

11. Liquid A has a density of 0.7 g/cm3. Liquid B has a density of 1.6 g/cm3. 140 g of liquid A and 128 g of liquid B are mixed to make liquid C. Work out the density of liquid C. .............................................. g/cm3

(4)

10. [4 marks]

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Feb by Maths4Everyone.com, Extra Q14: 4 Marks

-9-

10. 200g of aluminium and 200g of copper are mixed to make 400g of an alloy. Aluminium has a density of 2.7 g/cm3. Copper has a density of 8.9 g/cm3. Work out the density of the alloy. .............................................. g/cm3

(4)

11. Liquid A has a density of 0.7 g/cm3. Liquid B has a density of 1.6 g/cm3. 140 g of liquid A and 128 g of liquid B are mixed to make liquid C. Work out the density of liquid C. .............................................. g/cm3

(4)

11. [4 marks]

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Feb by Maths4Everyone.com, Extra Q15: 4 Marks

M V DAluminium 200g 74 07cm 2.7 g Ic

Copper 200g 22.47cm 8.9 g cm

400g 96.54

D My s 4.1451cm

4 14

M V DA 140g 200cm 0.7 glenB 128g 80cm t.bg cm3

268g 280cm

D My 22 0.957 g1cm

0.957

-10-

x. Brass is an alloy which is made by mixing copper and zinc. Copper has a density of 8.9 g/cm3. Zinc has a density of 7.1 g/cm3. 1 kilogram of brass is made by mixing 630 g of copper with 370 g of zinc. Work out the density of the brass. Give your answer correct to 1 decimal place. .............................................. g/cm3

(4)

12. [4 marks]

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Feb by Maths4Everyone.com, Extra Q16: 4 Marks

-5-

4. The diagram shows a solid triangular prism.

Diagram NOT accurately drawn

The prism is made from steel. The density of the steel is 7.9 grams per cm3. Calculate the mass of the prism. Give your answer in kilograms, correct to 3 significant figures. ........................................................

(3) 5. One sheet of A4 paper has dimensions 21.0 cm by 29.7 cm. The paper has a mass of 80 g per m2.

Work out the total mass of 500 sheets of A4 paper. Give your answer in kilograms, correct to 3 significant figures. ........................................................

(4)

8 cm

6 cm 11 cm

11 cm

5 cm 12 cm

13 cm

6 cm

5 cm

9 cm 4 cm

14 cm

9 cm 13 cm

12 cm

13. [4 marks]

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Feb by Maths4Everyone.com, Extra Q10: 4 Marks

M V DCopper 630g 70 79cm 8 gg c

Zine 370g 52.11cm 7 I glomBrass 1000g 122.90cm

D My 8.14122.9

8 14

One sheet 0.21 x 0.297 m20.06237 m2

Mass 80 0.06237 X 500 g500sheets

2494.8g2.49 Kg

2 49kg

-11-

12. Mia makes an orange drink by mixing orange concentrate with water. She mixes 15 ml of orange concentrate with 200 ml of water. The density of the orange concentrate is 1.24 g/cm3. The density of water is 1.00 g/cm3. Work out the density of Mia’s drink. Give your answer correct to 2 decimal places. .............................................. g/cm3

(3)

13. The density of apple juice is 1.05 grams per cm3. The density of fruit syrup is 1.4 grams per cm3. The density of carbonated water is 0.99 grams per cm3. 25 cm3 of apple juice are mixed with 15 cm3 of fruit syrup and 280 cm3 of carbonated water to make a drink with a volume of 320 cm3. Work out the density of the drink. Give your answer correct to 2 decimal places. .............................................. g/cm3

(4)

14. [4 marks]

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Feb by Maths4Everyone.com, Extra Q17: 4 Marks

-12-

12. Mia makes an orange drink by mixing orange concentrate with water. She mixes 15 ml of orange concentrate with 200 ml of water. The density of the orange concentrate is 1.24 g/cm3. The density of water is 1.00 g/cm3. Work out the density of Mia’s drink. Give your answer correct to 2 decimal places. .............................................. g/cm3

(3)

13. The density of apple juice is 1.05 grams per cm3. The density of fruit syrup is 1.4 grams per cm3. The density of carbonated water is 0.99 grams per cm3. 25 cm3 of apple juice are mixed with 15 cm3 of fruit syrup and 280 cm3 of carbonated water to make a drink with a volume of 320 cm3. Work out the density of the drink. Give your answer correct to 2 decimal places. .............................................. g/cm3

(4)

15. [4 marks]

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Feb by Maths4Everyone.com, Extra Q18: 4 Marks

M V DOrange 18.6g 15cm 1.24 glenWater 200g 200C 1.00 glenn

218.6g 215cm

D My 218 6215 1.021.0167

M V Dapple 26.25g 25cm 1.05 glamSyrup 21 S 15cm 1 A 51cmwater 277.2 as 280cm 0.99 glam

324.45g 320cm

D M

J324.45 1 013201.0139

-13-

14. The densities of two different liquids A and B are in the ratio 11 : 9 The mass of 1 ml of liquid B is 1.2 g. 10 ml of liquid A is mixed with 20 ml of liquid B to make 30 ml of liquid C. Work out the density of liquid C. .............................................. g/cm3

(4)

16. [5 marks]

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Feb by Maths4Everyone.com, Extra Q19: 5 Marks

-12-

14. The densities of two different liquids A and B are in the ratio 11:9 The mass of 1 ml of liquid B is 1.2 g. 10 ml of liquid A is mixed with 20 ml of liquid B to make 30 ml of liquid C. Work out the density of liquid C. .............................................. g/cm3

(4)

15. A solid snooker ball is made in the shape of a sphere. The ball has a mass of 156 g measured to the nearest gram.

Its diameter is 57 mm measured to the nearest millimetre. Find the lower bound for the density of the ball. Give your answer correct to 3 significant figures. .............................................. g/cm3

(4)

17. [5 marks]

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Feb by Maths4Everyone.com, Extra Q20: 5 Marks

Density B F I.zg cm3

Density A 1.2 X Ig 1.467 glow

M v DA 14.67g 10cm 1.467 gkn3B 24 g 20cm l Z glam

38.67g 30cm

D M 1.289j

38 6730 1.29 to 3sf

D Ivlower bound lowM

1555gE Mass 156.5g high56.5mL Dian L 57.5mm28 25mL radar L 28.75mm

lower D 155.5boo 1 fizzy

1.562 10 gym1.562 10

3 1000 glen

1 56

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16. A solid metal bar is made in the shape of a cuboid.

Diagram NOT accurately drawn

The cross-section of the bar is a square of side x cm. The length of the bar is y cm. The mass of the bar is M kg. x = 5.0 correct to 1 decimal place. y = 25 correct to the nearest whole number. M = 4.24 correct to 2 decimal places. Calculate the density of the metal, in g/cm3, that was used to make the bar. Give your answer to an appropriate degree of accuracy. ............................... g/cm3

(5)

x cm

x cm

y cm

18. [5 marks]

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Feb by Maths4Everyone.com, Extra Q21: 5 Marks

4 95 X 5.0524.5 E y 25.5

4.235 M 4.245

Max Vol 5.052 25 5 Min Vol 4.952 24.5

Max Density Max Mass 4 245 1000Min Vol 4.952 24.5

7.071 glen

Min Density MenMust 4.235 X 1000Max Vol 5.052 25 5

6.512 glenDensity 7 glam to nearest whole number

or to 1 Sigfig

-14-

x. A solid cone is made of wood.

Diagram NOT accurately drawn

The height of the cone is 18 cm. The mass of the cone is 0.98 kg The wood has a density of 0.43 g/cm3 Find the radius of the cone. Give your answer correct to 2 significant figures. .................................... cm

(5)

h

r r

18 cm

r cm

19. [5 marks]

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Feb by Maths4Everyone.com, Extra Q22: 5 Marks

Vol f n Th

Vol Masse 980Density 0.43

Vol 2279 cm's

2279 Ig r'x 182279 Z

TT

r J Gitr 10.99 cm

r Il cm

-15-

11. A solid sphere is made of glass.

Diagram NOT accurately drawn

The mass of the sphere is 58.4 g The density of the glass is 2.6 g/cm3 Find the diameter of the sphere. Give your answer correct to 3 significant figures. .................................... cm

(5)

5 cm

4 cm

0.3 cm

x cm

20. [5 marks]

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Feb by Maths4Everyone.com, Extra Q23: 5 Marks

Vol r

Voi Io 528

292I

it3

x 3 r 3

4T

r f 13 4Tr 1.75cm

-16-

x. A solid cube has a mass of 9.8 g. It has a density of 0.92 g/cm3. Find the surface area of the cube. Give your answer correct to 2 significant figures. ................................... cm2

(5)

21. [5 marks]

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Feb by Maths4Everyone.com, Extra Q24: 5 Marks

Vol E M 9.8 10.65217 cm

D 0.92

Edger X 5217

x 2.2 c

Each face 22

Surface area 6 2 6 2.2229.04 m2

29

-17-

x. A squash ball is made of rubber and is the shape of a sphere.

Diagram NOT accurately drawn

The mass of the ball 24 g. The external diameter of the ball is 40 mm. The thickness of the rubber is 4 mm. Assuming that the mass of air inside the ball is negligible, calculate the density of the rubber. ................................ g/cm3

(5)

5 cm

40 mm

4 mm

x cm

22. [5 marks]

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Feb by Maths4Everyone.com, Extra Q25: 5 Marks

External radius r 20mm

Internal radius Vz 16 mm

Vol of russia Ear Fitz4g 203 163

16353 mm

16.353 cm

Density My 76 1.47 glen

-18-

x. A 200 gallon steam kettle is used to make soup. The kettle is in the shape of a cylinder.

Diagram NOT accurately drawn

The kettle has a diameter of 1.2 m. The depth of the soup in the kettle is 67 cm. The density of the soup is 1.15 g/cm3. The soup is to be dispensed into tins that hold 400 g of soup each. How many tins can be filled with the soup from the kettle? You must show all your working. .........................................

(5)

1.2 m

67 cm

23. [5 marks]

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Feb by Maths4Everyone.com, Extra Q26: 5 Marks

radius60cm

Vol ITIL Tx 602 67 757752cm

M Vol Density Mass 757752 1.15

871415g871415 2178.5325400

2178 tins can be filled