$$\text{Density } \rho = \frac{\text{mass}}{\text{volume}} = \frac{m}{V} \qquad m = \rho V \qquad V = \frac{m}{\rho}$$

• $1\ \text{g/cm}^3 = 1000\ \text{kg/m}^3$.
• Volume: cuboid $= lwh$, cylinder $= \pi r^2 h$, sphere $= \tfrac{4}{3}\pi r^3$. Area of a circle $= \pi r^2$.
• $1\ \text{m}^3 = 10^6\ \text{cm}^3 = 1000$ litres; $1\ \text{cm}^3 = 1$ ml.
• Relative density $= \dfrac{\text{density of the substance}}{\text{density of water}}$.
• Thickness of one sheet (or diameter of one wire turn) $= \dfrac{\text{total thickness}}{\text{number of sheets}}$.
• Area of an oil film: thickness (molecule diameter) $d = \dfrac{V}{A}$.