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First teaching 2023

First exams 2025

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Density (CIE AS Physics)

Revision Note

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Leander

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Density

  • Density is the mass per unit volume of an object

rho space equals space m over V

  • Where:
    • ρ (the Greek letter rho) = density in kilograms per metre cubed (kg m-3)
    • m = mass in kilograms (kg)
    • V = volume in metres cubed (m3)

  • Gases are less dense than liquids, which are less dense than solids
  • This is because there are fewer particles, and therefore less mass, per unit volume

Relative density of a gas and a solid

Density comparison, downloadable AS & A Level Physics revision notes

Gases are less dense than solids because they have fewer particles, and therefore less mass, per unit volume

  • The volume of an object may not always be given directly, but can be calculated with the appropriate equation depending on the object’s shape

Calculating the volumes of different shapes

Volume of shapes, downloadable AS & A Level Physics revision notes

Expressions for calculating the volume of a sphere, a cube and a cylinder

Worked example

A paving slab has a mass of 73 kg and dimensions 40 mm × 500 mm × 850 mm.

Calculate the density, in kg m-3 of the material from which the paving slab is made.

WE - Density question image, downloadable AS & A Level Physics revision notes

Answer:

Step 1: List the known quantities and convert to SI units

  • Mass, m = 73 kg
  • Length, l = 0.850 m
  • Width, w = 0.500 m
  • Height, h = 0.040 m

Step 2: State the equation for density

rho space equals space m over V

Step 3: Calculate the volume

volume space of space straight a space cuboid space equals space length space cross times space width space cross times space height

V space equals space l w h

V space equals space 0.850 space cross times space 0.500 space cross times space 0.040

V space equals space 0.017 space straight m cubed

Step 4: Substitute the known values to calculate

rho space equals space fraction numerator 73 over denominator 0.017 end fraction

rho space equals space 4300 space kg space straight m to the power of negative 3 end exponent space open parentheses 2 space straight s. straight f. close parentheses

Examiner Tip

  • When converting a larger unit to a smaller one, you multiply (×)
    • E.g. 125 m = 125 × 100 = 12 500 cm

  • When you convert a smaller unit to a larger one, you divide (÷)
    • E.g. 5 g = 5 over 1000 = 0.005 or 5 × 10-3 kg

  • When dealing with squared or cubic conversions, cube or square the conversion factor too
    • E.g. 1 mm3 = 1 over 1000 cubed = 1 × 10-9 m3
    • E.g. 1 cm3 = 1 over 1000 cubed = 1 × 10-6 m3

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Leander

Author: Leander

Expertise: Physics

Leander graduated with First-class honours in Science and Education from Sheffield Hallam University. She won the prestigious Lord Robert Winston Solomon Lipson Prize in recognition of her dedication to science and teaching excellence. After teaching and tutoring both science and maths students, Leander now brings this passion for helping young people reach their potential to her work at SME.