What is Density?
Density measures how tightly packed the matter inside an object is.
- •If two objects have the exact same size (volume), the heavier one has a higher density (like a brick vs. a styrofoam block).
- •If two objects have the exact same weight (mass), the smaller one has a higher density.
The DMV Density Triangle
You can instantly rearrange the density formula by picturing the DMV Triangle:
Useful Unit Fact:
In science:
One milliliter of liquid takes up the exact same physical space as a cubic centimeter cube!
Worked Example 1: Finding Density with Water Displacement
When an object has an irregular shape (like a rock or a ring), you cannot measure its length with a ruler. Instead, you drop it into a graduated cylinder of water and measure how much the water rises!
Problem:
A mineral specimen has a mass of 75 grams.
A student drops it into a graduated cylinder filled with 50 mL of water. The water level rises to 65 mL.
What is the density of the mineral?
Step 1: Find the volume of the mineral (Water Displacement)
Step 2: Apply the density formula (D = mV)
The density of the mineral is 5.0 g/cm3.
Worked Example 2: Solving for Volume (V = mD)
Problem:
Pure gold has a known density of 19.3 g/cm3.
A jewelry maker has a bar of pure gold with a mass of 96.5 grams.
What is the volume of this gold bar?
Step 1: Rearrange for Volume
Using our DMV Triangle, cover V:
Step 2: Plug in the values
The volume of the gold bar is 5.0 cm3 (or 5.0 mL).
Sinking vs. Floating in Water
Pure liquid water has a density of exactly 1.0 g/cm3 (or 1.0 g/mL).
- •Density < 1.0 g/cm3: The object floats (e.g. wood, ice at 0.92 g/cm3, oil).
- •Density > 1.0 g/cm3: The object sinks (e.g. aluminum at 2.7 g/cm3, iron, gold).
- •Density = 1.0 g/cm3: Neutral buoyancy (suspends in the middle).
Density Quick Reference Table
| Material | Density (g/cm3) | Will it Float in Water? |
|---|---|---|
| Air | 0.0012 | Yes (rises) |
| Gasoline | 0.68 | Yes (floats on top) |
| Ice | 0.92 | Yes (floats with 90% submerged) |
| Liquid Water | 1.00 | Benchmark |
| Aluminum | 2.70 | No (sinks) |
| Iron / Steel | 7.87 | No (sinks) |
| Lead | 11.34 | No (sinks) |
| Gold | 19.32 | No (sinks very fast) |
Density Never Changes with Size!
A tiny drop of pure water has a density of 1.0 g/mL, and an entire Olympic swimming pool of pure water has a density of 1.0 g/mL. Density is an intensive physical property—cutting an object in half cuts both its mass and volume in half, keeping density unchanged!