Density, Mass & Volume Cheat Sheet

Key Facts

• Density is calculated with $\rho = \frac{m}{V}$, where $\rho$ is density, $m$ is mass, and $V$ is volume.
• Mass can be found by rearranging the density formula as $m = \rho V$.
• Volume can be found by rearranging the density formula as $V = \frac{m}{\rho}$.
• Common density units include $\text{g}/\text{cm}^3$, $\text{g}/\text{mL}$, and $\text{kg}/\text{m}^3$.
• For water, $1\ \text{mL} = 1\ \text{cm}^3$, so density in $\text{g}/\text{mL}$ can match density in $\text{g}/\text{cm}^3$.
• The volume of a rectangular solid is $V = lwh$, where $l$ is length, $w$ is width, and $h$ is height.
• An irregular object's volume can be measured by water displacement using $V_{\text{object}} = V_{\text{final}} - V_{\text{initial}}$.
• An object floats if $\rho_{\text{object}} < \rho_{\text{fluid}}$ and sinks if $\rho_{\text{object}} > \rho_{\text{fluid}}$.

Vocabulary

Density

Density is the amount of mass in a given volume, calculated with $\rho = \frac{m}{V}$.

Mass

Mass is the amount of matter in an object, usually measured in grams or kilograms.

Volume

Volume is the amount of space an object or substance takes up, often measured in $\text{cm}^3$, $\text{mL}$, or $\text{L}$.

Water Displacement

Water displacement is a method for finding volume by measuring how much the water level rises when an object is submerged.

Buoyancy

Buoyancy is the upward force a fluid exerts on an object placed in it.

Material Property

A material property is a characteristic, such as density, that helps identify a substance and does not depend on sample size.