Key Terms
- Density: The mass packed into a unit volume of a substance
- Mass: The amount of matter in an object (measured in g or kg)
- Volume: The amount of space an object occupies (measured in cm³ or m³)
- Units (density): g/cm³ or kg/m³
- Floating: An object floats if its density is less than 1 g/cm³ (less dense than water)
Must-Know Facts
- Density = Mass ÷ Volume
- Mass = Density × Volume
- Volume = Mass ÷ Density
- Water has density 1 g/cm³ — objects with density < 1 float
- 1 g/cm³ = 1000 kg/m³
- Always include units in your answer
Key Formulas
- D = M ÷ V
- M = D × V
- V = M ÷ D
- Use the DMV triangle: cover the unknown to find the formula
Common Mistakes
- Unit mismatch: Density in g/cm³ requires mass in g and volume in cm³ — don't mix with kg/m³
- Formula inversion: D = M ÷ V (not M ÷ D or V ÷ M) — use the triangle to check
- Volume of irregular objects: Use displacement method — volume = water level rise in cm³
- Confusing mass and weight: Mass is in kg/g; weight is a force in N — density uses mass
This topic summary covers Knowledge Organiser: Density within Density for GCSE Mathematics. Revise Density in Ratio & Proportion for GCSE Mathematics with 14 exam-style questions and 3 flashcards. This is a high-frequency topic, so it is worth revising until the explanation feels precise and repeatable. It is section 6 of 6 in this topic. Use this topic summary to connect the idea to the wider topic before moving on to questions and flashcards.
Practice questions for Density
Which formula correctly shows how density (D), mass (M) and volume (V) are related?
Explain what is meant by a density of 5 g/cm³.
Quick recall flashcards
Density Formula
Density = Mass ÷ Volume. Units: g/cm³ or kg/m³. Cover what you need in the triangle!
Floating Rule
Objects float if their density is LESS than the liquid. Water = 1 g/cm³, so anything under 1 g/cm³ floats.