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Density, Mass and Volume - Edexcel GCSE Higher Maths

Typically 2-5 marks per paper · Spec 1MA1

Density sits in the ratio and proportion strand of Edexcel's 1MA1 specification, under R1 for units and R11 for the measures built out of them. The relationship is density=massvolume\text{density} = \frac{\text{mass}}{\text{volume}}, and pressure is the identical piece of arithmetic with force where the mass was and area where the volume was. Both are common content, so Foundation candidates meet them as well; what marks the Higher versions out is that the volume is rarely handed to you, and the units rarely match first time. Speed comes from the same two spec references and is dealt with on its own page.

All three papers can carry it. On Paper 1, where no calculator is allowed, the numbers divide cleanly and the setting is often pressure on a rectangular base: a force in newtons, base measurements you have to turn into an area, one division. Papers 2 and 3 are where a cylinder, a sphere, a hemisphere or a triangular prism has to be worked out before the density formula is touched at all, and where the answer needs rounding. The Exam Aid sheet issued with 1MA1 papers for the 2025 to 2027 series gives you the volume of a prism and the circle formulae, but not density=massvolume\text{density} = \frac{\text{mass}}{\text{volume}}; a pressure question sometimes prints its own relationship in the stem, though nothing entitles you to expect that.

Most of the marks that go missing here are lost to units rather than to method. A density in g/cm3^3 wants the mass in grams, so 0.5 kg becomes 500 g before anything is divided, and a base given in centimetres becomes metres before it meets a force in newtons. The second repeat offender is the alloy question: when two metals are melted together the density of the mixture is the total mass divided by the total volume, and averaging the two densities gives a number that is wrong every time the two volumes differ. Write the substitution on its own line, keep the full display on the calculator, and round once.

Worked example

A solid cylinder has radius 3 cm and height 10 cm. The cylinder is made of a metal of density 8.9 g/cm3^3. Work out the mass of the cylinder in kg, correct to 2 decimal places.
[4 marks]
  1. V=πr2h=π×32×10V = \pi r^2 h = \pi \times 3^2 \times 10
    M1: correct substitution into the volume of a cylinder
  2. V=90π=282.743...V = 90\pi = 282.743... cm3^3
    A1: the volume, left unrounded or as a multiple of π\pi
  3. mass=density×volume=8.9×282.743...=2516.4...\text{mass} = \text{density} \times \text{volume} = 8.9 \times 282.743... = 2516.4... g
    M1: density multiplied by volume, units still grams and cm3^3
  4. 2516.4... g=2.5164... kg=2.522516.4... \text{ g} = 2.5164... \text{ kg} = 2.52 kg
    A1: 2.52, after dividing by 1000 and rounding once at the end

Practice questions

These are original questions in Edexcel 1MA1 Higher style. The opening ones use the relationship in all three directions with matching units; later questions make you find the volume of a cuboid, cylinder, prism, cone or sphere first, switch between g/cm3^3 and kg/m3^3, or combine two materials. Where a rounding is stated, keep the unrounded value on your calculator until the last line.

No account needed: the questions below are always free to check, plus 8 extra questions today. Your score so far updates as you go.

  1. Question 1 Warm-up [2 marks]
    Silver has density 10.5 g/cm3^3. Work out the mass, in grams, of a piece of silver of volume 40 cm3^3.
  2. Question 2 Exam pace [2 marks]
    A solid cuboid measures 5 cm by 4 cm by 3 cm. The cuboid has mass 300 g. Work out the density of the cuboid, in g/cm3^3.
  3. Question 3 Exam pace [3 marks]
    A solid prism has a cross-section that is a right-angled triangle whose two shorter sides are 6 cm and 8 cm. The prism is 15 cm long and has mass 1.08 kg. Work out the density of the prism, in g/cm3^3.
  4. Question 4 Stretch [3 marks]
    A box rests on a horizontal floor. The base of the box is a rectangle measuring 40 cm by 25 cm. The box exerts a force of 600 N on the floor. Work out the pressure on the floor, in N/m2^2.
  5. Question 5 Stretch [3 marks]
    A crate rests on a horizontal floor and exerts a force of 720 N on it. The pressure on the floor is 400 N/m2^2. The base of the crate is a rectangle of width 1.2 m. Work out the length of the base, in metres.
  6. Question 6 Stretch [4 marks]
    A solid cylinder has radius 4 cm and mass 2.4 kg. The cylinder is made of a metal of density 7.5 g/cm3^3. Work out the height of the cylinder in cm, correct to 1 decimal place.

Common mistakes examiners see

  • Dividing the volume by the mass, so a block of mass 240 g and volume 60 cm3^3 comes out at 0.25 g/cm3^3 instead of 4 g/cm3^3.

    Read the units of the answer: g/cm3^3 means grams divided by cubic centimetres, so the mass goes on top. If the number you get is smaller than 1 for a piece of metal, you have divided the wrong way round.

  • Leaving the mass in kilograms while the density is in g/cm3^3, so 0.5 kg divided by 19.3 gives 0.0259 rather than a volume of 25.9 cm3^3.

    Convert first, on its own line: 0.5 kg = 500 g. Match the mass unit to the top of the density unit and the volume unit to the bottom before you substitute anything.

  • Changing g/cm3^3 into kg/m3^3 by multiplying by 100 or by dividing by 1000, turning 2.5 g/cm3^3 into 250 or 0.0025.

    Do the two conversions separately: 1 g becomes 0.001 kg and 1 cm3^3 becomes 0.000001 m3^3, and 0.001÷0.000001=10000.001 \div 0.000001 = 1000. So multiply by 1000 going to kg/m3^3 and divide by 1000 coming back.

  • Averaging the densities of two metals in an alloy question, giving 8 g/cm3^3 for 200 g of a 4 g/cm3^3 metal melted with 300 g of a 12 g/cm3^3 metal instead of 6.67 g/cm3^3.

    Find each volume from mass divided by density, add the masses, add the volumes, then divide once. The mean of the two densities is only right when the two volumes are equal, which the numbers in an exam question are chosen to avoid.

  • Working out the pressure under a box by multiplying the force by the base area, or by using a base in centimetres, so a 600 N box on a 40 cm by 25 cm base gives 600000 rather than 6000 N/m2^2.

    Pressure is force divided by area, so the bigger the base the smaller the answer. Convert each length to metres before multiplying: 40 cm by 25 cm is 0.4 m by 0.25 m, an area of 0.1 m2^2.

Frequently asked questions

Is the density formula given in the Edexcel GCSE maths exam?
No. The Exam Aid formulae sheet issued with 1MA1 papers for the 2025 to 2027 series covers areas, volumes of prisms, circles, trigonometry, the quadratic formula, compound interest and probability, not the compound measures. You have to recall density=massvolume\text{density} = \frac{\text{mass}}{\text{volume}} and rearrange it yourself. A pressure question will sometimes state its relationship in the stem, but write it down from memory anyway.
How do you convert g/cm3 to kg/m3?
Multiply by 1000. A gram is a thousandth of a kilogram and a cubic centimetre is a millionth of a cubic metre, and dividing those two factors leaves a scale factor of 1000. So 2.5 g/cm3^3 is 2500 kg/m3^3, and 7800 kg/m3^3 is 7.8 g/cm3^3.
Is density on the Foundation paper as well as Higher?
Yes. R11 is common content, so a Foundation paper can ask for a density, a mass or a volume directly. The Higher tier versions add a step in front: the volume has to be found from a cylinder or a sphere, the mass arrives in kilograms when the density is in g/cm3^3, or two materials are combined and you need the total mass over the total volume.
How many marks is a density or pressure question worth on Edexcel Higher?
Usually 2-5 marks per paper. A single substitution is worth 2 or 3 marks, and one that hides a volume calculation, a unit change or an alloy runs to 4 or 5. Density also appears inside other questions, most often bounds work, where an upper bound for a density comes from the upper bound of the mass over the lower bound of the volume.

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