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This table shows the mass and volume of four different objects.

\begin{tabular}{|c|c|}
\hline
Object & Measurements \\
\hline
W & \begin{tabular}{l}
Mass: [tex]$16 g$[/tex] \\
Volume: [tex]$84 cm ^3$[/tex]
\end{tabular} \\
\hline
X & \begin{tabular}{l}
Mass: [tex]$12 g$[/tex] \\
Volume: [tex]$5 cm ^3$[/tex]
\end{tabular} \\
\hline
Y & \begin{tabular}{l}
Mass: [tex]$4 g$[/tex] \\
Volume: [tex]$6 cm ^3$[/tex]
\end{tabular} \\
\hline
Z & \begin{tabular}{l}
Mass: [tex]$408 g$[/tex] \\
Volume: [tex]$216 cm ^3$[/tex]
\end{tabular} \\
\hline
\end{tabular}

Which ranks the objects from most to least dense?

A. [tex]$X, Y, W, Z$[/tex]
B. [tex]$X, Z, Y, W$[/tex]
C. [tex]$W, Y, Z, X$[/tex]
D. [tex]$Z, Y, X, W$[/tex]



Answer :

GinnyAnswer
To determine which ranks the objects from most to least dense, start by calculating the density for each object. Density can be calculated using the formula:
[tex]\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \][/tex]

Given the measurements:

- Object W:
[tex]\[ \text{Mass} = 16 \, \text{g}, \, \text{Volume} = 84 \, \text{cm}^3 \][/tex]
[tex]\[ \text{Density} = \frac{16 \, \text{g}}{84 \, \text{cm}^3} \approx 0.1905 \, \text{g/cm}^3 \][/tex]

- Object X:
[tex]\[ \text{Mass} = 12 \, \text{g}, \, \text{Volume} = 5 \, \text{cm}^3 \][/tex]
[tex]\[ \text{Density} = \frac{12 \, \text{g}}{5 \, \text{cm}^3} = 2.4 \, \text{g/cm}^3 \][/tex]

- Object Y:
[tex]\[ \text{Mass} = 4 \, \text{g}, \, \text{Volume} = 6 \, \text{cm}^3 \][/tex]
[tex]\[ \text{Density} = \frac{4 \, \text{g}}{6 \, \text{cm}^3} \approx 0.6667 \, \text{g/cm}^3 \][/tex]

- Object Z:
[tex]\[ \text{Mass} = 408 \, \text{g}, \, \text{Volume} = 216 \, \text{cm}^3 \][/tex]
[tex]\[ \text{Density} = \frac{408 \, \text{g}}{216 \, \text{cm}^3} \approx 1.8889 \, \text{g/cm}^3 \][/tex]

Now, list the densities:
- Object W: [tex]\( 0.1905 \, \text{g/cm}^3 \)[/tex]
- Object X: [tex]\( 2.4 \, \text{g/cm}^3 \)[/tex]
- Object Y: [tex]\( 0.6667 \, \text{g/cm}^3 \)[/tex]
- Object Z: [tex]\( 1.8889 \, \text{g/cm}^3 \)[/tex]

Next, sort the objects by their densities in descending order (from the highest to the lowest):

1. Object X: [tex]\( 2.4 \, \text{g/cm}^3 \)[/tex]
2. Object Z: [tex]\( 1.8889 \, \text{g/cm}^3 \)[/tex]
3. Object Y: [tex]\( 0.6667 \, \text{g/cm}^3 \)[/tex]
4. Object W: [tex]\( 0.1905 \, \text{g/cm}^3 \)[/tex]

Thus, the correct ranking from most to least dense is:
[tex]\[ X, Z, Y, W \][/tex]

Therefore, the correct answer is:
[tex]\[ \boxed{X, Z, Y, W} \][/tex]

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