Let's solve this problem step-by-step:
1. Find the density of the unknown element:
The volume of the unknown element is given as [tex]\( 16 \)[/tex] cubic inches and the weight is [tex]\( 4.13 \)[/tex] pounds.
The density of a material is calculated using the formula:
[tex]\[
\text{Density} = \frac{\text{Weight}}{\text{Volume}}
\][/tex]
So, we plug in the given values:
[tex]\[
\text{Density} = \frac{4.13 \, \text{pounds}}{16 \, \text{cubic inches}} = 0.258125 \, \text{lb/in}^3
\][/tex]
2. Compare the calculated density with the given densities in the table:
\begin{tabular}{|l|l|}
\hline \text{Element} & \text{Density} ([tex]$\text{lb/in}^3$[/tex]) \\
\hline Titanium & 0.161 \\
\hline Zinc & 0.258 \\
\hline Iron & 0.284 \\
\hline Silver & 0.379 \\
\hline
\end{tabular}
The calculated density of [tex]\( 0.258125 \, \text{lb/in}^3 \)[/tex] is very close to the density of Zinc, which is [tex]\( 0.258 \, \text{lb/in}^3 \)[/tex].
3. Select the element with the closest matching density:
Since [tex]\( 0.258125 \, \text{lb/in}^3 \)[/tex] is almost identical to [tex]\( 0.258 \, \text{lb/in}^3 \)[/tex], the unknown element is Zinc.
Therefore, the correct answer is:
[tex]\[
\boxed{\text{B. Zinc}}
\][/tex]
