How Crowded is Matter?

Why it matters

A kilogram of iron and a kilogram of cotton weigh exactly the same — but one hides in your fist and one fills a pillow. The difference has a number, and the number has a name.

The idea in plain words

The identification recipe. Tap the steps.

ρ = m ÷ V

A stone of 54 g raises the water level from 40 mL to 60 mL. Density?

2.7 g/cm³ — that 'stone' is aluminium!

• g or kg: mass — from a beam balance
• cm³ or m³: volume — regular solid: measure and multiply · irregular: displacement in a measuring cylinder
• the conversion: unit trap — 1 g/cm³ = 1000 kg/m³ — water is 1 in one unit and 1000 in the other
• V = 60 − 40 = 20 cm³
• ρ = 54 ÷ 20

Predict first

Density is…

Heavy and dense are different: a ship is heavy but not dense; a coin is light but dense. Density asks how TIGHTLY the mass is packed.

• mass packed per unit volume: ρ = m/V — correct
• how heavy something is
• how big something is

What you do

Dunk each mystery block — the water's RISE is its volume. Divide mass by volume and unmask all three metals. (Careful: the rise, not the level!)

Check yourself

To find an irregular stone's volume you use…

The stone shoves aside exactly its own volume of water — read the rise.

The S.I. unit of density is…

g/cm³ is handy in the lab, but S.I. speaks kg/m³ (water: 1000).

Two cubes, same size; one is cork, one is lead. The lead cube has…

Same V, wildly different m — density is the m/V ratio, not the size.

• the rise of water level in a measuring cylinder — correct
• length × breadth × height
• a beam balance
• kg/m³ — correct
• g/cm³
• kg/m²
• more mass in the same volume — higher density — correct
• more volume
• the same density — same size