The radius of the Earth is approximately 6370 km. If one could dig down straight towards the center of the Earth, one would find that the outermost 2890 km (the crust and the mantle) has an average density of about 4.5 g/cm3. Farther down is the core. If the average density of the Earth is 5.5 g/cm3, what is the average density of the Earth's core? (Recall that the volume of a sphere is given by V = (4/3)πr3.)

volume of earth is 4/3 pi * 6370^3 = 10.8270*10^11 km^3

volume of core is 4/3 pi * (6370-2890)^3 = 1.7653*10^11 km^3
volume of crust+mantle is thus 9.0617*10^11 km^3

5.5*10.8270*10^11 = 4.5*9.0617*10^11 + d*1.7653*10^11
d = 10.6 g/cm^3

10.63

Please find my questions in your office 6390km

To find the average density of the Earth's core, we need to calculate the volume and mass of the outermost layer (crust and mantle) and subtract it from the total volume and mass of the Earth to determine the volume and mass of the core.

First, let's calculate the volume and mass of the outermost 2890 km (crust and mantle):
1. Calculate the volume of the outermost layer using the formula for the volume of a sphere: V = (4/3)πr³.
- Radius of the outermost layer = 6370 km
- Volume of the outermost layer = (4/3)π(6370 km)³

2. Calculate the mass of the outermost layer using the density formula: Mass = Density × Volume.
- Density of the outermost layer = 4.5 g/cm³
- Volume of the outermost layer (converted to cm³) = Volume of the outermost layer × (1 km / 100000 cm)³
- Mass of the outermost layer = Density of the outermost layer × Volume of the outermost layer (converted to cm³)

Next, let's calculate the volume and mass of the core by subtracting the volume and mass of the outermost layer from the total volume and mass of the Earth:

3. Calculate the volume of the Earth using the formula for the volume of a sphere: V = (4/3)πr³.
- Radius of the Earth = 6370 km
- Volume of the Earth = (4/3)π(6370 km)³

4. Calculate the mass of the Earth using the average density formula: Mass = Density × Volume.
- Average density of the Earth = 5.5 g/cm³
- Volume of the Earth (converted to cm³) = Volume of the Earth × (1 km / 100000 cm)³
- Mass of the Earth = Average density of the Earth × Volume of the Earth (converted to cm³)

Finally, we can determine the volume and mass of the core:

5. Volume of the core = Volume of the Earth - Volume of the outermost layer
6. Mass of the core = Mass of the Earth - Mass of the outermost layer

7. Calculate the density of the core using the formula: Density = Mass / Volume.
- Density of the core = Mass of the core / Volume of the core

Perform the calculations using the given values and formulas to find the average density of the Earth's core.