Answer
\[\underline{\text{7}\text{.6 g/c}{{m}^{3}}\text{ }}\]
Work Step by Step
Radius of cylinder is in inches (in); convert it into centimeter (cm) as follows:
\[\begin{align}
& 1\text{ in}=\text{2}\text{.54 cm} \\
& r=\frac{\left( 0.22\text{ in} \right)\left( \text{2}\text{.54 cm} \right)}{1\text{ in}} \\
& =0.559\text{ cm}
\end{align}\]
Similarly, length of cylinder is in inches (in); convert it into centimeters (cm) as follows:
\[\begin{align}
& 1\text{ in}=\text{2}\text{.54 cm} \\
& l=\frac{\left( \text{2}\text{.16 in} \right)\left( \text{2}\text{.54 cm} \right)}{1\text{ in}} \\
& =5.49\text{ cm}
\end{align}\]
Calculate volume of cylinder as follows:
\[\begin{align}
& V=\pi {{r}^{2}}l \\
& =\left( \frac{22}{7} \right){{\left( 0.559\text{ cm} \right)}^{2}}\left( 5.49\text{ cm} \right) \\
& =5.39\text{ c}{{\text{m}}^{3}}
\end{align}\]
Calculate density as follows:
\[\begin{align}
& d=\frac{m}{V} \\
& =\frac{41\text{ g}}{5.39\text{ c}{{\text{m}}^{3}}} \\
& =7.6\text{ g/c}{{\text{m}}^{3}}
\end{align}\]
Density of steel is \[\underline{\text{7}\text{.6 g/c}{{\text{m}}^{3}}\text{ }}\].
