IGCSEMathsCambridge (CIE)ExtendedRevision NotesNumberCompound Measures (Speed, Density, Pressure)Speed, Density & Pressure

Speed, Density & Pressure (Cambridge (CIE) IGCSE Maths)

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Naomi C

Written by: Naomi C

Reviewed by: Dan Finlay

Cambridge (CIE) Maths: ExtendedEdexcel Maths A (Modular): Higher Unit 1Cambridge (CIE) Maths: CoreCambridge (CIE) International Maths: ExtendedCambridge (CIE) International Maths: Core

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Speed, Density & Pressure

What are speed, density and pressure?

  • Speed, density and pressure are frequently used compound measures

    • Speed is equal to distance divided by time

    • Density is equal to mass divided by volume

    • Pressure is equal to force divided by area

Formula Triangles for Speed, Density and Pressure

What should I know about speed, distance and time?

  • Speed is commonly measured in metres per second (m/s) or kilometres per hour (km/h)

    • The units indicate speed is distance per time
      Speed equals Distance over Time

  • 'Speed' (in this formula) means 'average speed'

  • In harder problems there are often two journeys or two parts to one longer journey

What should I know about density, mass and volume?

  • Density is usually measured in grams per centimetre cubed (g/cm3) or kilograms per metre cubed (kg/m3)

    • The units indicate that density is mass per volume
      Density equals Mass over Volume

  • You may need to use a volume formula to find the volume of an object first

What should I know about pressure, force and area?

  • Pressure is usually measured in Newtons per square metre (N/m2)

    • The units of pressure are often called Pascals (Pa) rather than N/m2

    • The units indicate that pressure is force per area
      Pressure equals Force over Area

  • Remember that weight is a force

    • It is different to mass

Examiner Tips and Tricks

  • Look out for a mixture of units

    • Time can be given as minutes but common phrases like 'half an hour' (30 minutes) could also be used in the same question

    • Any mixed units should be those in common use and easy to convert, e.g., g to kg or m to km etc

Worked Example

A box exerts a force of 140 newtons on a table.
The pressure on the table is 35 newtons/m2.

p equals F over A        p space equals space pressure F space equals space force A space equals space area

Calculate the area of the box that is in contact with the table.

Method 1

Substitute the numbers you know into the formula

35 space equals space 140 over A      

Solve the equation for A
First multiply both sides by A to get A out of the denominator

35 A equals 140

Then divide by 35 to find the value of A

table row cell A space end cell equals cell space 140 over 35 space end cell end table

The units will be m2, matching the units seen in newtons/m2

4 m2 

Method 2

Use the given formula to create a formula triangle for pressure, force and area

space space F p space space space space space space A      

A is on the bottom of the triangle, so this tells us to divide F by P

A space equals space F over p space equals space 140 over 35 space equals space 4      

4 m2

Worked Example

The density of pure gold is 19.3 g/cm3.

What is the volume of a gold bar that has a mass of 0.454 kg? 

Begin by checking that all of the units are consistent
Density is given in g/cm3
Convert the volume of the gold bar into grams to match the units

0.454 kg = (0.454 × 1000) g = 454 g

The units of density are g/cm3, so divide the mass (g) by the volume (cm3)

Or, write out the formula triangle

Formula triangle: Mass, Density, Volume

Write out the formula that you will need

Volume space equals fraction numerator space mass over denominator density end fraction

Substitute the given values for the mass and the density

Volume space space equals space fraction numerator space 454 over denominator 19.3 end fraction space equals space 23.5233...

Make sure you give the correct units with your final answer
The density is given in g/cm3, so the volume should be cm3

Volume = 23.5 cm3 (1 d.p.)

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    Author
    Reviewer
    Naomi C

    Author: Naomi C

    Expertise: Maths

    Naomi graduated from Durham University in 2007 with a Masters degree in Civil Engineering. She has taught Mathematics in the UK, Malaysia and Switzerland covering GCSE, IGCSE, A-Level and IB. She particularly enjoys applying Mathematics to real life and endeavours to bring creativity to the content she creates.

    Dan Finlay

    Author: Dan Finlay

    Expertise: Maths Lead

    Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.