The mass of the earth is known to be about 5.98 X10^24kg assume that it is approx. spherical with an average diameter of 1.276X10^7 METERS. from these data calculate the average density of the earth(g/cm^3) could the earth be made mostly of water (density=1.00g/cm^3), abundant elements like calcium silicate (density=3.27g/cm^3) or aluminum oxide(density=4.0g/cm^3)?

How do I explain this????What hypothesis would explain why the earth has a considerably higher density than any of these materials, which are abundant at the surface of the earth???

i got 2.88g/cm^3 for the earths density. is that right?

I did not get 2.88 g/cc as a density but I could have made an error.

I used 4/3(*pi*r^3) for volume and converted diameter in m to cm first.
I converted mass in kg to grams first.
For the explanation, what is the core of the earth. If that is made of something much more dense it would make the overall density more than the surface area. Post your work if you want me to check the density calculation.

http://www.universetoday.com/26771/density-of-the-earth/

See this link for the inner core.

http://en.wikipedia.org/wiki/Earth

To calculate the average density of the Earth, we can use the formula:

Density = Mass / Volume

First, we need to find the volume of the Earth. Since the Earth is approximately a sphere, we can use the formula for the volume of a sphere:

Volume = (4/3) * π * (radius)^3

The average diameter of the Earth is given as 1.276X10^7 meters, so the radius would be half of that: 6.38 X 10^6 meters.

Plugging these values into the formula, we can calculate the volume:

Volume = (4/3) * π * (6.38 X 10^6)^3

Next, we can determine the mass of the Earth, which is given as 5.98 X 10^24 kg.

Now we can calculate the density using the formula:

Density = Mass / Volume

Density = (5.98 X 10^24 kg) / [(4/3) * π * (6.38 X 10^6)^3]

Calculating this expression, we find that the average density of the Earth is approximately 5.52 g/cm^3, not 2.88 g/cm^3 as you mentioned.

Now, let's discuss why the Earth's density is considerably higher than materials like water (density = 1.00 g/cm^3), calcium silicate (density = 3.27 g/cm^3), or aluminum oxide (density = 4.0 g/cm^3).

The higher density of the Earth can be explained by the fact that it is composed of a variety of different materials, not just a single substance like water or the mentioned abundant elements. The Earth's interior is primarily made up of dense metallic elements like iron and nickel, which have much higher densities compared to materials found on the Earth's surface.

The Earth's core, for example, consists mostly of iron and nickel, and these materials have densities around 8-13 g/cm^3. The presence of these dense materials in the core contributes significantly to the overall average density of the Earth.

In contrast, water, calcium silicate, and aluminum oxide are relatively lighter materials that are more commonly found on the Earth's surface. These materials, although abundant, do not account for the majority of the Earth's composition, especially in the core region.

Therefore, the Earth's considerably higher density than materials like water, calcium silicate, or aluminum oxide can be explained by its diverse composition, with a significant portion consisting of denser metallic elements in the core.

In summary, the average density of the Earth is approximately 5.52 g/cm^3, and it cannot be mainly composed of water or other abundant surface materials with lower densities due to the presence of denser metallic elements in its core.