\section{Measurement of the density of solids}
\subsection{Theory}
The density of regularly shaped solids can be determined by measuring their mass, m, and
calculating their volume, $V$. The density, $\rho$, can then be found using:
\[ \rho = \frac{m}{V}\]
\subsection{Apparatus}
\begin{itemize}
\item Various regularly shaped solids both rectangular and circular,
\item 30 cm ruler (resolution \SI{\pm 0.1}{cm})
\item Vernier calipers / micrometer (resolution \SI{\pm 0.01}{mm})
\item Balance (resolution \SI{\pm 0.1}{g})
\end{itemize}
\subsection{Experimental Method}
Determine the mass of the object using the balance.
The volume of a rectangle can be found by measuring the length, $l$, width, $w$, and height, $h$. Calculate the volume, $V$ using:
\[V = l w h\]
The volume of a sphere is found by measuring the diameter to find the radius, r, and then calculate the volume using: \[ V= \frac{4}{3} \pi r^{3}\] \sidenote{Irregular shapes are harder to measure, so we use the Archimedian principle and a water displacement can to measure the volume. If faced with a buoyant object you can weigh it down with another object, so long as you subtract the volume of that weight from the total volume of water displaced.}
\begin{marginfigure}
\includegraphics{eurekacan.png}
\caption{Displacement can in use.}
\end{marginfigure}
In both cases calculate the density using: $ \rho = m/V$.