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Calculating density and measuring volume

I can define density, calculate its value, and describe how to measure volume.

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New

Calculating density and measuring volume

I can define density, calculate its value, and describe how to measure volume.

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Lesson details

Key learning points

Density is calculated using the equation: density = mass ÷ volume.
Density is measured in kg/m³ or g/cm³.
The volume of water displaced by a submerged object is equal to the volume of the object.
The dimensions of a regular cuboid can be measured accurately with Vernier callipers.
The volume of a regular cuboid is calculated using the equation: volume = length × width × height.

Keywords

Density - the mass per cubic metre (m³) or cubic centimetre (cm³) of a material
Kilograms per cubic metre - the unit for density when mass is measured in kilograms (kg) and volume in cubic metres (m³), written as kg/m³
Grams per cubic centimetre - the unit for density when mass is measured in grams (g) and volume in cubic centimetres (cm³), written as g/cm³
Vernier callipers - a device used to measure length precisely
Micrometer - a device used to measure length to a very high precision

Common misconception

Pupils confuse the mass or weight of an object with density.

Provide pupils with a range of objects of varying sizes they are going to measure the density of and, before starting to do so, ask the pupils to rank the objects in order of density with explanations. Compare results to the list after measurements.

Demonstrate the use of callipers carefully to the pupils. Digital callipers can make measurements much easier. Show the pupils how to check for zero errors with measuring instruments.

Teacher tip

Equipment

Licence

This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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Prior knowledge starter quiz

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6 Questions

Q1.
Which of the following quantities does a measuring cylinder measure?

area

mass

height

Correct answer: volume

Q2.
Which of the following quantities means ‘amount of matter’?

weight

Correct answer: mass

volume

charge

Q3.
Here is a mathematical formula: $$c=\frac{d}{e}$$. Rearrange the formula to make $$d$$ the subject.

$$d=\frac{c}{e}$$

$$d=\frac{e}{c}$$

Correct answer: $$d=ec$$

Q4.
Here is a mathematical formula: $$f=\frac{g}{h}$$. Rearrange the formula to make $$h$$ the subject.

$$h=\frac{f}{g}$$

Correct answer: $$h=\frac{g}{f}$$

$$h=gf$$

Q5.
On the left is a set of numbers. On the right are the same numbers after rounding to three significant figures. Match each number on the left with its rounded value on the right.

Correct Answer:7.955,7.96

7.96

Correct Answer:7.946,7.95

7.95

Correct Answer:7.9449,7.94

7.94

Correct Answer:7.9032,7.90

7.90

Correct Answer:7.999,8.00

8.00

Q6.
A pupil observes that a beetle runs 5.0 m in 3.0 s, and uses the formula speed = distance ÷ time to calculate the speed. Which of the following is the most accurate way to write the beetle’s speed?

1.6 m/s

2 m/s

Correct answer: 1.7 m/s

1.67 m/s

1.666666667 m/s

Assessment exit quiz

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6 Questions

Q1.
Which of the following instruments are used to measure length?

Correct answer: Vernier callipers

displacement can

Correct answer: micrometer

microammeter

measuring cylinder

Q2.
A displacement can contains water up to its spout. An object is placed in the water and sinks. A beaker collects the water that flows from the spout. Which of the following statements is correct?

The mass of water collected equals the mass of the object.

Correct answer: The volume of water collected equals the volume of the object.

The density of water collected equals the density of the object.

Q3.
A paper clip has mass 1.2 g and volume 0.15 cm³. What is the density of the paper clip in g/cm³?

0.13 g/cm³

0.18 g/cm³

1.4 g/cm³

Correct answer: 8.0 g/cm³

14 g/cm³

Q4.
The diagram shows a Vernier scale. The marking on the lower scale that lines up most closely with a marking on the upper scale has been circled. The reading on the scale is cm.

Correct Answer: 7.46, 7.46 cm, 7.46cm

Q5.
The density of diamond is 3500 kg/m³. What is the density of diamond in g/cm³?

Correct answer: 3.5 g/cm³

350 g/cm³

3500 g/cm³

35 000 g/cm³

3 500 000 g/cm³

Q6.
The metal osmium is the densest element that occurs naturally on Earth, with density 22.6 g/cm³. The mass of a cube of osmium with side length 3.00 cm is g. Give you answer to 3 sig. fig.

Correct Answer: 610, 610 g, 610g

Lesson appears in

UnitCombined science / Particle explanations of density and pressure

UnitPhysics / Particle explanations of density and pressure

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EdexcelPhysics

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AQAPhysics

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Calculating density and measuring volume

Calculating density and measuring volume

Lesson slides

Lesson details

Key learning points

Keywords

Common misconception

Equipment

Licence

Lesson video

Worksheet

Prior knowledge starter quiz

6 Questions

Q1.Which of the following quantities does a measuring cylinder measure?

Q2.Which of the following quantities means ‘amount of matter’?

Q3.Here is a mathematical formula: $$c=\frac{d}{e}$$. Rearrange the formula to make $$d$$ the subject.

Q4.Here is a mathematical formula: $$f=\frac{g}{h}$$. Rearrange the formula to make $$h$$ the subject.

Q5.On the left is a set of numbers. On the right are the same numbers after rounding to three significant figures. Match each number on the left with its rounded value on the right.

Q6.A pupil observes that a beetle runs 5.0 m in 3.0 s, and uses the formula speed = distance ÷ time to calculate the speed. Which of the following is the most accurate way to write the beetle’s speed?

Assessment exit quiz

6 Questions

Q1.Which of the following instruments are used to measure length?

Q2.A displacement can contains water up to its spout. An object is placed in the water and sinks. A beaker collects the water that flows from the spout. Which of the following statements is correct?

Q3.A paper clip has mass 1.2 g and volume 0.15 cm³. What is the density of the paper clip in g/cm³?

Q4.The diagram shows a Vernier scale. The marking on the lower scale that lines up most closely with a marking on the upper scale has been circled. The reading on the scale is cm.

Q5.The density of diamond is 3500 kg/m³. What is the density of diamond in g/cm³?

Q6.The metal osmium is the densest element that occurs naturally on Earth, with density 22.6 g/cm³. The mass of a cube of osmium with side length 3.00 cm is g. Give you answer to 3 sig. fig.

Lesson appears in

UnitCombined science / Particle explanations of density and pressure

EdexcelCombined science

OCRCombined science

AQACombined science

UnitPhysics / Particle explanations of density and pressure

OCRPhysics

EdexcelPhysics

AQAPhysics

Q1.
Which of the following quantities does a measuring cylinder measure?

Q2.
Which of the following quantities means ‘amount of matter’?

Q3.
Here is a mathematical formula: $$c=\frac{d}{e}$$. Rearrange the formula to make $$d$$ the subject.

Q4.
Here is a mathematical formula: $$f=\frac{g}{h}$$. Rearrange the formula to make $$h$$ the subject.

Q5.
On the left is a set of numbers. On the right are the same numbers after rounding to three significant figures. Match each number on the left with its rounded value on the right.

Q6.
A pupil observes that a beetle runs 5.0 m in 3.0 s, and uses the formula speed = distance ÷ time to calculate the speed. Which of the following is the most accurate way to write the beetle’s speed?

Q1.
Which of the following instruments are used to measure length?

Q2.
A displacement can contains water up to its spout. An object is placed in the water and sinks. A beaker collects the water that flows from the spout. Which of the following statements is correct?

Q3.
A paper clip has mass 1.2 g and volume 0.15 cm³. What is the density of the paper clip in g/cm³?

Q4.
The diagram shows a Vernier scale. The marking on the lower scale that lines up most closely with a marking on the upper scale has been circled. The reading on the scale is cm.

Q5.
The density of diamond is 3500 kg/m³. What is the density of diamond in g/cm³?

Q6.
The metal osmium is the densest element that occurs naturally on Earth, with density 22.6 g/cm³. The mass of a cube of osmium with side length 3.00 cm is g. Give you answer to 3 sig. fig.