Answer
\[\underline{\text{0}\text{.77 in}}\]
Work Step by Step
Calculate volume of aluminum as follows:
\[\begin{align}
& V=\frac{m}{d} \\
& =\frac{\text{85 g}}{\text{2}\text{.7 g/c}{{\text{m}}^{3}}} \\
& =31.48\text{ c}{{\text{m}}^{3}}
\end{align}\]
Calculate volume of cylinder as follows:
\[\begin{align}
& V=\frac{4}{3}\pi {{r}^{3}} \\
& r={{\left( \frac{3V}{4\pi } \right)}^{1/3}} \\
& ={{\left( \frac{\left( 3 \right)\left( 31.48\text{ c}{{\text{m}}^{3}} \right)}{\left( 4 \right)\left( 22/7 \right)} \right)}^{^{1/3}}} \\
& =1.958\text{ cm}
\end{align}\]
Radius is in centimeter (cm); convert it into inches (in) as follows:
\[\begin{align}
& 1\text{ cm}=\text{0}\text{.3937 in} \\
& \text{1}\text{.958 cm}=\left( \text{1}\text{.958 cm} \right)\left( \frac{\text{0}\text{.3937 in}}{1\text{ cm}} \right) \\
& =0.77\text{ in}
\end{align}\]
