To determine the densities of rocks in different layers of the Earth, let's calculate the average density for each layer using the given densities at the top and bottom for each layer.
1. Crust:
- Top density: [tex]\(2.2 \, g/cm^3\)[/tex]
- Bottom density: [tex]\(2.9 \, g/cm^3\)[/tex]
- Average density: [tex]\(\frac{2.2 + 2.9}{2} = 2.55 \, g/cm^3\)[/tex]
2. Upper Mantle:
- Top density: [tex]\(3.4 \, g/cm^3\)[/tex]
- Bottom density: [tex]\(4.4 \, g/cm^3\)[/tex]
- Average density: [tex]\(\frac{3.4 + 4.4}{2} = 3.90 \, g/cm^3\)[/tex]
3. Lower Mantle:
- Top density: [tex]\(4.4 \, g/cm^3\)[/tex]
- Bottom density: [tex]\(5.6 \, g/cm^3\)[/tex]
- Average density: [tex]\(\frac{4.4 + 5.6}{2} = 5.00 \, g/cm^3\)[/tex]
Given these calculated average densities, we find:
- Average density of the crust: [tex]\(2.55 \, g/cm^3\)[/tex]
- Average density of the upper mantle: [tex]\(3.90 \, g/cm^3\)[/tex]
- Average density of the lower mantle: [tex]\(5.00 \, g/cm^3\)[/tex]
From these values, we observe that as we go deeper into the Earth, the density increases. The lower mantle has a higher average density than the upper mantle, and the upper mantle has a higher average density than the crust.
Since the information about the core’s density isn't explicitly given but knowing that the core is composed of very dense materials like iron and nickel, we can conclude that the core is the densest layer. Therefore, the correct conclusion is:
The rocks in the core are the most dense.
