Sheet № 118 · Foundation + Higher · AQA · Edexcel · OCR
Density, Mass & Volume –
Density, mass and volume questions appear on both Foundation and Higher GCSE papers. Density is a compound measure that connects how heavy something is to how much space it takes up. The formula triangle works identically to speed-distance-time, so once you master one, the other follows naturally. This guide covers the formulas, unit conv
§Key definitions
Density
measures how much mass is packed into a given volume. A material with high density, such as lead, has a lot of mass in a small volume. A material with low density, such as cork, has relatively little mass for its size.
Question:
A block of metal has a mass of 540 g and a volume of 200 cm³. Calculate the density.
Answer:
The density of the metal is 2.7 g/cm³.
Q1 (Foundation):
A stone has a mass of 300 g and a volume of 120 cm³. Find its density.
Q2 (Foundation):
A liquid has a density of 1.2 g/cm³. A container holds 500 cm³ of the liquid. Find the mass.
§Formulas to memorise
Density = Mass ÷ Volume
Mass = Density × Volume
Volume = Mass ÷ Density
Identify — which quantity you need to find (density, mass, or volume).
Check units — ensure mass and volume units are compatible with the density unit.
Substitute — into the correct rearrangement of the formula.
Calculate — and include the correct unit in your answer.
Worked example
A block of metal has a mass of 540 g and a volume of 200 cm³. Calculate the density.
Working: Density = Mass ÷ Volume Density = 540 ÷ 200 = 2.7 g/cm³.
⚠ Common mistakes
- ✗Mixing up units. If density is in kg/m³ and volume is in cm³, you must convert one before calculating. 1 m³ = 1,000,000 cm³ and 1 kg = 1,000 g.
- ✗Forgetting to calculate volume first. Many exam questions give dimensions of a shape rather than the volume directly. Work out the volume before using D = M/V.
- ✗Inverting the formula. Density = Mass ÷ Volume, not Volume ÷ Mass. Use the formula triangle: M on top, D and V on the bottom.
- ✗Rounding volume too early. When the volume involves π, keep the exact value until the final step to avoid rounding errors.
✦ Exam tips
- →Draw the formula triangle (M at the top, D × V at the bottom) in your working. It helps you rearrange correctly and earns method marks.
- →If the question involves a composite shape, find the total volume by adding or subtracting component volumes before applying the density formula.
- →Always state the unit of your final answer — density questions carry a unit mark.
- →Remember the key conversion: 1 g/cm³ = 1000 kg/m³. This comes up when questions switch between metric units.
- →On multi-step questions, calculate the volume first and write it down before moving to the density calculation.