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.
Knowledge Organiser: Density
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
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.