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Using the measurements in the table, determine which unidentified metal has the lowest density.

\begin{tabular}{|c|c|c|}
\hline
Metal & Volume & Mass \\
\hline
A & [tex]$12.5 \, \text{cm}^3$[/tex] & [tex]$122 \, \text{g}$[/tex] \\
\hline
B & [tex]$14.2 \, \text{cm}^3$[/tex] & [tex]$132 \, \text{g}$[/tex] \\
\hline
C & [tex]$18.1 \, \text{cm}^3$[/tex] & [tex]$129 \, \text{g}$[/tex] \\
\hline
D & [tex]$12.7 \, \text{cm}^3$[/tex] & [tex]$126 \, \text{g}$[/tex] \\
\hline
\end{tabular}

A. Metal A

B. Metal B

C. Metal C

D. Metal D



Answer :

GinnyAnswer
To identify which metal has the lowest density, we need to calculate the density of each metal using their given volumes and masses. Density is calculated as \(\text{Density} = \frac{\text{Mass}}{\text{Volume}}\).

Let's go through the calculations step-by-step for each metal:

1. Metal A:
- Volume: \(12.5 \; cm^3\)
- Mass: \(122 \; g\)
- Density\( = \frac{Mass}{Volume} = \frac{122 \; g}{12.5 \; cm^3} = 9.76 \; g/cm^3\)

2. Metal B:
- Volume: \(14.2 \; cm^3\)
- Mass: \(132 \; g\)
- Density\( = \frac{Mass}{Volume} = \frac{132 \; g}{14.2 \; cm^3} \approx 9.30 \; g/cm^3\)

3. Metal C:
- Volume: \(18.1 \; cm^3\)
- Mass: \(129 \; g\)
- Density\( = \frac{Mass}{Volume} = \frac{129 \; g}{18.1 \; cm^3} \approx 7.13 \; g/cm^3\)

4. Metal D:
- Volume: \(12.7 \; cm^3\)
- Mass: \(126 \; g\)
- Density\( = \frac{Mass}{Volume} = \frac{126 \; g}{12.7 \; cm^3} \approx 9.92 \; g/cm^3\)

Now we have the densities of all metals:
- Metal A: \(9.76 \; g/cm^3\)
- Metal B: \(9.30 \; g/cm^3\)
- Metal C: \(7.13 \; g/cm^3\)
- Metal D: \(9.92 \; g/cm^3\)

From these calculations, we can see that the metal with the lowest density is Metal C, which has a density of approximately \(7.13 \; g/cm^3\).

Therefore, the unidentified metal with the lowest density is Metal C.

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