Density
Mass per unit volume.
Formula
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Example
A 200 g block of 250 cm³: ρ = 200/250 = 0.8 g/cm³ (it floats).
How it works
Density tells you how tightly matter is packed into a given space. It works by comparing an object's mass to the amount of space it occupies, so two objects with the same volume can have very different densities if one contains more mass. A higher density means more mass in each unit of volume, while a lower density means the material is more spread out.
When to use it
Use this formula when you need to find the density of a substance or object from its mass and volume. It is common in problems about floating and sinking, identifying materials, and comparing how compact different substances are.
Worked example, step by step
A metal cube has a mass of 540 g and a volume of 180 cm³. Step 1: Write the formula: ρ = m / V Step 2: Substitute the values: ρ = 540 g / 180 cm³ Step 3: Divide: ρ = 3 g/cm³ Final answer: The density of the cube is 3 g/cm³.
Common mistakes to avoid
- Using the wrong units, such as mixing grams with cubic metres without converting first
- Dividing volume by mass instead of mass by volume
- Forgetting that density must be reported with units such as kg/m³ or g/cm³
Did You Know?
A block of osmium is so dense a fist-sized piece weighs over 5 kg; ice, by contrast, floats on its own liquid.
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