\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$.