Density is a measure of how much mass is contained in a given volume. It tells us how tightly packed the matter is in an object.
Density is calculated by dividing an object's mass by its volume. The formula is:
Where:
The most common units for density are:
| Material | Density ($g/cm^3$) |
|---|---|
| Air | 0.0012 |
| Water (pure) | 1.00 |
| Ice | 0.92 |
| Wood (Oak) | 0.60 - 0.90 |
| Aluminum | 2.70 |
| Iron | 7.87 |
| Gold | 19.32 |
An object's density determines if it will sink or float in a liquid. An object will float if its density is less than the liquid's density. An object will sink if its density is greater than the liquid's density.
Will this object sink or float in water? (Water density: $1.0 \, g/cm^3$)
The volume of the block is its length multiplied by its width and height.
$$V_{\text{block}} = 10 \times 5 \times 4 = 200 \, cm^3$$
The volume of a cylinder is $\pi$ times the radius squared times its height.
$$V_{\text{hole}} = \pi r^2 h = \pi (1 \, cm)^2 (10 \, cm) \approx 31.42 \, cm^3$$
Subtract the volume of the hole from the volume of the block.
$$V_{\text{final}} = V_{\text{block}} - V_{\text{hole}} = 200 - 31.42 = 168.58 \, cm^3$$
Use the density formula with the given mass and the final volume.
$$\rho = \frac{m}{V_{\text{final}}} = \frac{1250 \, g}{168.58 \, cm^3} \approx 7.41 \, g/cm^3$$
The density of the material is approximately $7.41 \, g/cm^3$. This is very close to the density of iron ($7.87 \, g/cm^3$), so the block is likely made of iron or an iron alloy.
Different liquids and solids can be layered based on their density. The least dense material floats on top, and the most dense sinks to the bottom.
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