Density Quiz (Grade 5)

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Score: 0 / 10

Density — Notes & Worked Examples Show / Hide

Explanation:

Density, mass and volume are linked by Density = MassVolume, Mass = Density × Volume, and Volume = MassDensity. Check the units carefully: if density is in g/cm³, mass must be in grams (1 kg = 1000 g) and volume in cm³.

When two metals or liquids are mixed together, never average the two densities—always work out the Total Mass and Total Volume separately, then use Combined Density = Total MassTotal Volume.

Example 1: A solid metal block has volume 350 cm³ and density 8.4 g/cm³. Find its mass in kilograms.

Solution:

Mass = Density × Volume

Mass = 8.4 × 350 = 2940 g

Convert grams to kilograms (÷ 1000):

2940 ÷ 1000 = 2.94 kg

Answer: 2.94 kg

Example 2: Liquid A (180 g, density 0.9 g/cm³) is mixed with Liquid B (420 g, density 1.4 g/cm³). Find the density of the mixture.

Solution:

Vol A = 180 ÷ 0.9 = 200 cm³; Vol B = 420 ÷ 1.4 = 300 cm³

Total Mass = 180 + 420 = 600 g

Total Volume = 200 + 300 = 500 cm³

Mixture Density = 600 ÷ 500 = 1.2 g/cm³

Answer: 1.2 g/cm³

One Page Guide (PDF) Density Worksheets

Question 1

[1 mark]

A block of wood has a volume of 40cm³ and a mass of 20g
Calculate its density

g/cm³

Worked Solution & Answer

(Density = mass ÷ volume) B1

Answer: 0.5 g/cm³ g/cm³

Question 2

[1 mark]

A piece of metal has a density of 9 g/cm³ and a volume of 15cm³
Calculate its mass

Worked Solution & Answer

(Density = mass ÷ volume) B1

Answer: 135g g

Question 3 IGCSE Jan 2023 2FR Q24

[3 marks]

The diagram shows two solids, **A** and **B**, made from two different metals.

Solid **A** is in the shape of a cylinder with radius 3 cm and height 7 cm
Solid **A** has a mass of 2000 g
Solid **B** has a mass of 3375 g
Solid **B** has a volume of 450 cm³
All of the metal from Solid **A** and Solid **B** is melted down to make a uniform Solid **C**
Given that there is no change to mass or volume during this process
work out the density of Solid **C**
Give your answer correct to one decimal place.

g / cm³

Worked Solution & Answer

(The volume of a cylinder is πr²h)
Volume of Solid A = π × 3² × 7 = 63π ≈ 197.92 cm³ M1
Total mass = 2000 + 3375 = 5375 g M1
Total volume = 63π + 450 ≈ 647.92 cm³
Density = 5375 ÷ 647.92 = 8.2957... = 8.3 g/cm³. A1

Answer: 8.3 g / cm³

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Question 4 IGCSE Jun 2022 1FR Q23

[3 marks]

The diagram shows a solid cylinder made from iron.

The cylinder has diameter 18 cm and height 3.5 cm
The mass of the cylinder is 7.04 kg
Work out the density of the iron.
Give your answer in g/cm³ correct to 2 significant figures.

g/cm³

Worked Solution & Answer

(Density = mass ÷ volume)
Volume = π × 9² × 3.5 = 283.5π ≈ 890.64 cm³ M1
Mass = 7040 g M1
Density = 7040 ÷ 890.64 = 7.904… = 7.9 g/cm³ (2 s.f.) A1

Answer: 7.9 g/cm³

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Question 5 IGCSE Jun 2023 1FR Q27

[3 marks]

The diagram shows a block of iron in the shape of a cuboid.

The block has length w cm, width 5 cm and height 4 cm
The density of iron is 7.8 g/cm³
The mass of the block is 1950 g
Work out the value of w

w =

Worked Solution & Answer

(Density = mass ÷ volume)
Volume = Mass ÷ Density = 1950 ÷ 7.8 = 250 cm³ M2
5 × 4 × w = 250 ⇒ 20w = 250 ⇒ w = 12.5 A1

Answer: w = 12.5

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Question 6

[3 marks]

Here are two cubes, **A** and **B**.

Cube **A** has a mass of 81 g.
Cube **B** has a mass of 128 g.
Work out
[INDENT]the density of cube **A** : the density of cube **B**
Give your answer in the form a : b, where a and b are integers.

Worked Solution & Answer

(Density = mass ÷ volume)
Volume A = 3³ = 27 cm³ ⇒ density A = 81 ÷ 27 = 3 g/cm³ M1
Volume B = 4³ = 64 cm³ ⇒ density B = 128 ÷ 64 = 2 g/cm³ M1
Ratio = 3 : 2 A1

Answer: 3 : 2

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Question 7 IGCSE Jun 2024 1FR Q21

[4 marks]

The diagram shows a solid wooden cylinder.
The cylinder has radius 8 cm and height h cm.
The volume of the cylinder is 1208 cm³

(a) Work out the value of h
Give your answer correct to the nearest whole number. [2 marks]

h =

(b) Work out the mass of the cylinder.
Give your answer in kilograms. [2 marks]

kilograms

Worked Solution & Answer

(a)

(The volume of a cylinder is πr²h)
π × 8² × h = 1208 M1
⇒ h = 1208 ÷ (64π) = 6.008... ≈ 6 A1

Answer (a): h = 6

(b)

(The volume of a cylinder is πr²h)
Mass = 1208 × 1.25 = 1510 g = 1.51 kg M1 A1

Answer (b): 1.51 kilograms

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Question 8 OCR Nov 2022 4H Q6

[4 marks]

Work out
(a) A solid block of wood is a cuboid which measures 3 cm by 4 cm by 5 cm.
Its density is 0.65 g/cm³.
Work out the mass of the block of wood.
(b) Here are two areas.

(a) A solid block of wood is a cuboid which measures 3 cm by 4 cm by 5 cm.
Its density is 0.65 g/cm³.
Work out the mass of the block of wood. [2 marks]

(b) Here are two areas. [2 marks]

State which area is greater.
Show how you decide.

Worked Solution & Answer

(a)

Volume = 3 × 4 × 5 = 60 cm³ M1
Mass = density × volume = 0.65 × 60 = 39 g. A1

Answer (a): 39 g

(b)

(Density = mass ÷ volume)
1 m² = 1000² mm² = 1 000 000 mm². M1
0.12 m² = 120 000 mm² > 95 000 mm² (or 95 000 mm² = 0.095 m² < 0.12 m²), so Area A is greater. C1

Answer (b): Area A is greater because 0.12 m² = 120 000 mm², which is greater than 95 000 mm².

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Question 9 IGCSE Jan 2020 1FR Q23

[5 marks]

Pablo made a solid gold statue.
He melted down some gold blocks and used the gold to make the statue.
Each block of gold was a cuboid, as shown below.

The mass of the statue is 5.73 kg.
The density of gold is 19.32 g/cm³
Work out the least number of gold blocks Pablo melted down in order to make the statue.
Show your working clearly.

Worked Solution & Answer

(Density = mass ÷ volume)
Volume of 1 block = 1.5 × 2 × 8 = 24 cm³ M2
Mass of 1 block = 24 × 19.32 = 463.68 g M2
Number of blocks = 5730 ÷ 463.68 = 12.357... ⇒ 13 blocks A1

Answer: 13

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Question 10 AQA Nov 2022 3H Q14

[5 marks]

Here are two solid cubes, X and Y.
The mass of X is 10.976 kg
The area of **each face** of X is 784 cm²

(a) Zayan wants to know the density of Y.
He assumes that Y is identical to X.
What density should he get for Y?
Give your answer in **grams per cubic centimetre**. [4 marks]

Answer g/cm³

(b) In fact,
the mass of Y is less than the mass of X
the area of each face of Y is greater than the area of each face of X.
What does this mean about the actual density of Y?
Tick **one** box.
[ ] It is less than the answer to part (a)
[ ] It is equal to the answer to part (a)
[ ] It is greater than the answer to part (a)
[ ] It is not possible to tell [1 mark]

Worked Solution & Answer

(a)

(Density = mass ÷ volume)
Side length of X = √784 = 28 cm M1
Volume of X = 28³ = 21 952 cm³ M1
Mass in grams = 10.976 × 1000 = 10 976 g M1
Density = 10 976 ÷ 21 952 = 0.5 g/cm³ A1

Answer (a): Answer 0.5 g/cm³

(b)

(Density = mass ÷ volume)
Smaller mass divided by a larger volume gives a smaller density B1

Answer (b): It is less than the answer to part (a)

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Score: 0 / 10 (0 / 32 marks)

Density Worksheets Next: Pressure →

Grade 5 Quizzes

25 Topics

5A - Combining ratios	5B - Direct and inverse proportion
5C - Reverse percentages	5D - Standard form
5E - Speed	5F - Changing the subject
5G - Quadratic expressions	5H - Solving quadratic equations
5J - Drawing quadratic graphs	5K - Cubic/reciprocal graphs
5L - Simultaneous equations	5M - Sector areas and arc lengths
5N - Sim. equ. graphically	5P - Midpoint of a line segment
5Q - Gradient of a line	5R - Equation of a line
5S - Spheres and cones	5T - Similar shapes (lengths)
5U - Trigonometry (SOHCAHTOA)	5V - Exact trig. values
5W - Probability trees	5X - Vectors
5Y - Venn diagrams	5Z - Density
5AA - Pressure