To determine the identity of the unknown element based on its volume and weight, follow these detailed steps:
1. Calculate the density of the unknown element:
[tex]\[
\text{Density} = \frac{\text{Weight}}{\text{Volume}}
\][/tex]
Given:
[tex]\[
\text{Weight} = 4.13 \text{ pounds}
\][/tex]
[tex]\[
\text{Volume} = 16 \text{ cubic inches}
\][/tex]
Plug these values into the formula:
[tex]\[
\text{Density} = \frac{4.13 \text{ lb}}{16 \text{ in}^3} = 0.258125 \text{ lb/in}^3
\][/tex]
2. Compare the calculated density with the known densities from the table:
\begin{tabular}{|l|l|}
\hline Density & [tex]$lb / in ^3$[/tex] \\
\hline Titanium & 0.161 \\
\hline Zinc & 0.258 \\
\hline Iron & 0.284 \\
\hline Silver & 0.379 \\
\hline
\end{tabular}
The calculated density is:
[tex]\[
0.258125 \text{ lb/in}^3
\][/tex]
3. Identify the element:
- Compare [tex]\(0.258125 \text{ lb/in}^3\)[/tex] with the provided densities.
- The density [tex]\(0.258125 \text{ lb/in}^3\)[/tex] is closest to the density of Zinc, which is [tex]\(0.258 \text{ lb/in}^3\)[/tex].
4. Make the conclusion:
- Since the calculated density (0.258125 lb/in^3) is very close to the density of Zinc (0.258 lb/in^3), the unknown element is most likely Zinc.
The correct answer is:
[tex]\[
\boxed{\text{D. Zinc}}
\][/tex]
