Density, pressure and compound units

The units of a compound measure describe its quotient. Density is mass per unit volume: \(\rho=\dfrac mV\). Pressure is force per unit area: \(p=\dfrac FA\). Rearrange the quotient to find a total, and use compatible units.

Example

A block of mass \(540\text{ g}\) and volume \(200\text{ cm}^3\) has density \(2.7\text{ g/cm}^3\). Since one gram is \(0.001\text{ kg}\) and one cubic centimetre is \(10^{-6}\text{ m}^3\), this is \(2700\text{ kg/m}^3\).

A force of \(120\text{ N}\) over \(0.03\text{ m}^2\) exerts pressure \(4000\text{ N/m}^2\). Doubling the contact area halves the pressure if the force stays fixed.

Convert area or volume with squared or cubed length factors. Dividing by a smaller positive area makes pressure larger, which provides a direction check.