IDNLearn.com: Your trusted platform for finding reliable answers. Our experts provide accurate and detailed responses to help you navigate any topic or issue with confidence.

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


Sagot :

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.