Looking for trustworthy answers? Westonci.ca is the ultimate Q&A platform where experts share their knowledge on various topics. Discover in-depth solutions to your questions from a wide range of experts on our user-friendly Q&A platform. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.

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

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

Which ranks the objects from most to least dense?

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

Sagot :

To determine the ranking of the objects from most to least dense, we will first calculate the densities of each object using the formula for density:

[tex]\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \][/tex]

Here are the given values:
- Object [tex]\( W \)[/tex]: Mass [tex]\( = 16 \, \text{g} \)[/tex], Volume [tex]\( = 84 \, \text{cm}^3 \)[/tex]
- Object [tex]\( X \)[/tex]: Mass [tex]\( = 12 \, \text{g} \)[/tex], Volume [tex]\( = 5 \, \text{cm}^3 \)[/tex]
- Object [tex]\( Y \)[/tex]: Mass [tex]\( = 4 \, \text{g} \)[/tex], Volume [tex]\( = 6 \, \text{cm}^3 \)[/tex]
- Object [tex]\( Z \)[/tex]: Mass [tex]\( = 408 \, \text{g} \)[/tex], Volume [tex]\( = 216 \, \text{cm}^3 \)[/tex]

Let's calculate the density for each object:

1. Density of [tex]\( W \)[/tex]:
[tex]\[ \text{Density}_W = \frac{16 \, \text{g}}{84 \, \text{cm}^3} \approx 0.190476 \, \text{g/cm}^3 \][/tex]

2. Density of [tex]\( X \)[/tex]:
[tex]\[ \text{Density}_X = \frac{12 \, \text{g}}{5 \, \text{cm}^3} = 2.4 \, \text{g/cm}^3 \][/tex]

3. Density of [tex]\( Y \)[/tex]:
[tex]\[ \text{Density}_Y = \frac{4 \, \text{g}}{6 \, \text{cm}^3} \approx 0.666667 \, \text{g/cm}^3 \][/tex]

4. Density of [tex]\( Z \)[/tex]:
[tex]\[ \text{Density}_Z = \frac{408 \, \text{g}}{216 \, \text{cm}^3} \approx 1.888889 \, \text{g/cm}^3 \][/tex]

Now, let's rank the objects from most to least dense:
- [tex]\( X \)[/tex]: [tex]\( 2.4 \, \text{g/cm}^3 \)[/tex]
- [tex]\( Z \)[/tex]: [tex]\( \approx 1.888889 \, \text{g/cm}^3 \)[/tex]
- [tex]\( Y \)[/tex]: [tex]\( \approx 0.666667 \, \text{g/cm}^3 \)[/tex]
- [tex]\( W \)[/tex]: [tex]\( \approx 0.190476 \, \text{g/cm}^3 \)[/tex]

Thus, the correct ranking of objects from most to least dense is:

[tex]\[ X, Z, Y, W \][/tex]

So, the correct answer is:

[tex]\[ \boxed{X, Z, Y, W} \][/tex]
Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.