**Volume (V)** is defined as the amount of space occupied by a three-dimensional object as measured in cubic units.

- SI unit of volume is metres cube ($m^{3}$). It is a scalar quantity.

**Density** ($\rho$) is defined as the mass (m) of a substance per unit volume.

- SI unit of density is kilograms per metre cube (kg m
^{-3}). It is a scalar quantity. - Another common unit of density is $\text{g cm}^{-3}$.
- Note: $1000 \text{ kg m}^{-3} = 1 \text{ g cm}^{-3}$

Density is given by:

$$\rho = \frac{m}{V}$$

The density of a substance does not change as you move from place to place as the mass and volume does not depend on the gravitational acceleration of the point that the object is at.

## Self-Test Questions

### Examine the figure above. Why does the cork float and the rock sink in water?

**Show/Hide Answer**

The density of a substance determines whether it will float or sink in different liquids (or gases).

The cork is less dense than water $\rightarrow$ it floats in water.

The rock is denser than water $\rightarrow$ it sinks in water.

### A block of concrete with dimensions 0.4 m, 0.3 m and 0.1 m has a density of $2500 \text{ kg m}^{-3}$. Calculate the mass of the block.

**Show/hide answer**

The volume of the block is given by:

$$\begin{aligned} V &= 0.4 \times 0.3 \times 0.1 \\ &= 0.012 \text{ m}^{3} \end{aligned}$$

From the density equation ($\rho = \frac{m}{V}$), we have:

$$\begin{aligned} m &= \rho V \\ &= 2500 \times 0.012 \\ &= 30 \text{ kg} \end{aligned}$$