Rearrange density equations and convert cubic units
Find mass or volume and convert g/cm³ to kg/m³ using a cubic length conversion.
Core and Extended; Physics 0625, 2026–2028, section 1.4. Density is mass per unit volume. Match the units before calculating. The syllabus includes measuring liquid, regular-solid and sinking irregular-solid densities, then using density data to predict floating. Paper exercises support practical reasoning but do not demonstrate supervised practical competence. Written practice is self-checked
Before you begin
- Rearrange a division equation.
- Cube the factor in a length-unit conversion.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
How many cm³ are in 1 m³?
What you will learn
- Use m = ρV and V = m/ρ.
- Convert density and volume units consistently.
Isolate the required quantity
From ρ = m/V, multiply by V to get m = ρV. A material of density 2.7 g/cm³ occupying 15 cm³ has mass 40.5 g. For mass 54 g at density 2.7 g/cm³, rearrange to V = m/ρ = 20 cm³.
Check units before substituting. Multiplying g/cm³ by cm³ leaves g. Dividing g by g/cm³ leaves cm³. If the volume is supplied in m³ while density is in g/cm³, convert one of them first rather than multiplying incompatible numerical values.
A cubic conversion uses the length factor three times
One metre is 100 cm, so one cubic metre contains 100³ = 1,000,000 cm³. Thus 1 cm³ = 10⁻⁶ m³. Also 1 g = 0.001 kg, so 1 g/cm³ = 0.001/10⁻⁶ = 1000 kg/m³. A density of 2.7 g/cm³ is 2700 kg/m³.
For a cross-check, 54 g becomes 0.054 kg and 20 cm³ becomes 0.000020 m³. Dividing gives 2700 kg/m³, the same density. Do not convert cm³ to m³ by dividing by only 100: that is a length conversion, not a volume conversion.
Pause and explain
What is 2.7 g/cm³ in kg/m³?
Worked example
Convert 2.7 g/cm³ to kg/m³ and find the volume of 54 g at that density.
Show the worked solution
- Multiply the density by 1000 to obtain 2700 kg/m³.
- Using the original matched units, V = 54/2.7.
- V = 20 cm³ = 0.000020 m³.
Answer 2700 kg/m³; 20 cm³ or 0.000020 m³.
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Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
Find the mass of 15 cm³ at density 2.7 g/cm³.
Give me a hint
Multiply density by volume with matching cubic-centimetre units.
Compare my reasoning
- Use m = ρV.
- 2.7 × 15 = 40.5.
- The remaining unit is g.
40.5 g.
Look for these in your work
- Rearrange correctly.
- Cancel volume units.
Find the volume of 54 g at 2.7 g/cm³, then express both density and volume in SI units.
Give me a hint
Calculate in matched units, then apply the mass and cubic-volume factors.
Compare my reasoning
- V = 54/2.7 = 20 cm³.
- Density is 2700 kg/m³.
- Volume is 20 × 10⁻⁶ = 0.000020 m³.
20 cm³; 2700 kg/m³; 0.000020 m³.
Look for these in your work
- Use m/ρ for volume.
- Apply the cubic conversion.
A liquid density is 800 kg/m³ and its volume is 250 ml. Find mass in kg and g.
Give me a hint
One ml equals one cm³; convert the volume into m³.
Compare my reasoning
- 250 ml = 250 cm³ = 0.000250 m³.
- m = 800 × 0.000250 = 0.200 kg.
- Convert to 200 g.
0.200 kg; 200 g.
Look for these in your work
- Convert the volume fully.
- Retain consistent density units.
Common mistakes
- Cube the length conversion for volume.
- A density conversion combines mass and volume factors.
- Use compatible units in m = ρV.
What can you explain now?
What mass occupies 15 cm³ at 2.7 g/cm³?
Compare with the explanation
40.5 g.
Multiply the density by the volume.
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Make it stick
Derive the g/cm³ to kg/m³ factor from its two unit conversions without memorising it alone.
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.