Question regarding earth's core and volume

[Remon]

The question simply asks (read slowly): What fraction of the earth’s volume is the molten part of the core?
I think I'm suppose to use the following equation since it has been stated in the book (though, I'm not entirely sure if I should):
surface area–to–volume ratio = (surface area)/(volume),
but that only includes the surface area, not the core which is what I'm looking for.
I also know that the Earth's density is 5.52 g/cm³, and we've also talked about the seismic waves in lectures (S- & P- waves) which might help me in figuring out the core's volume (or at least the molten part of it), which then I can use to compare to the Earth's volume (which I know is 1.08 x 10¹² km³), although, these waves don't give me any numbers to work with. Can someone please help connect all those "clues" together?

 

[gneill]

The question simply asks (read slowly): What fraction of the earth’s volume is the molten part of the core?
I think I'm suppose to use the following equation since it has been stated in the book (though, I'm not entirely sure if I should):
surface area–to–volume ratio = (surface area)/(volume),
but that only includes the surface area, not the core which is what I'm looking for.
I also know that the Earth's density is 5.52 g/cm³, and we've also talked about the seismic waves in lectures (S- & P- waves) which might help me in figuring out the core's volume (or at least the molten part of it), which then I can use to compare to the Earth's volume (which I know is 1.08 x 10¹² km³), although, these waves don't give me any numbers to work with. Can someone please help connect all those "clues" together?

Have a look at this page on The Interior of the Earth by the USGS.

Looks like you'll have to do some volume calculations...

 

[Remon]

Have a look at this page on The Interior of the Earth by the USGS.

Looks like you'll have to do some volume calculations...

I read the whole page, and while it does provide a lot of information, it doesn't have any equations relating to the core and the Earth's volume, but it does state the "thicknesses" of all of the sections of the Earth's interior, but not their volume.

 

[gneill]

I read the whole page, and while it does provide a lot of information, it doesn't have any equations relating to the core and the Earth's volume, but it does state the "thicknesses" of all of the sections of the Earth's interior, but not their volume.

Surely you can find the formula for the volume of a sphere from some resource at your disposal?

 

[Remon]

Surely you can find the formula for the volume of a sphere from some resource at your disposal?

Sorry, that's not what I meant before. I have that equation, but how do I use it to find the outer core's volume (so I can compare to the total volume of the Earth and find the ratio) when I'm not given the radius of the outer core (excluding the inner core's radius since the inner core is basically just "inside" of the outer core, so its hard to exclude its radius when calculating the outer core's radius) or any other information about it? thank you replying back by the way.

 

[haruspex]

Sorry, that's not what I meant before. I have that equation, but how do I use it to find the outer core's volume (so I can compare to the total volume of the Earth and find the ratio) when I'm not given the radius of the outer core (excluding the inner core's radius since the inner core is basically just "inside" of the outer core, so its hard to exclude its radius when calculating the outer core's radius) or any other information about it? thank you replying back by the way.

To get the material content of a hollow sphere, subtract the volume of the hollow from that of the full sphere.

 

[gneill]

You can always subtract a smaller volume from a larger volume if what's left is what you're interested in

 

[Remon]

You can always subtract a smaller volume from a larger volume if what's left is what you're interested in

Thank you both replying, I tried some calculations but I still get it wrong (I think), here's what I did:

I used the hollow sphere volume equation: 4∏/3 (R³ - r³) (I also tried the same formula with diameter instead) (I got the equation from this website: http://tinyurl.com/mwm4lr4)
Then I used this picture (http://tinyurl.com/kyaepdh) to find the radiuses/diameters that I need for the equation(s) (I'm trying to find area 5 in the picture because that's the outer core)
After finding the volume of the outer core (which was about 1.699 x 10¹¹ km³ from using the previous equations), I divided the total volume for Earth (which was 1.08 x 10¹² km³) by the volume I got for the outer core to find the ratio of the two volumes (and hopefully solve the question)
but then I got 6.something which was not one of the choices provided (all of the choices are decimals below 1), I checked the calculations again but it still gives me the same answer, maybe the ratio is wrong because the densities are different for each of the Earth's different interiors (such as the inner core having much higher density than any of the other "interiors", but I don't know if different densities change the volume)
Can you guys please help me again? this is due in a few days and its been driving crazy because its simple math but I somehow still get it wrong

 

[gneill]

After finding the volume of the outer core (which was about 1.699 x 10¹¹ km³ from using the previous equations), I divided the total volume for Earth (which was 1.08 x 10¹² km³) by the volume I got for the outer core to find the ratio of the two volumes (and hopefully solve the question)
but then I got 6.something

You want to know what fraction the liquid core is of the total. Thus the "total" goes in the denominator, and the fractional bit goes in the numerator.

It's like asking what fraction of a dollar does one penny represent; You don't say it's 100/1.

 

[Remon]

You want to know what fraction the liquid core is of the total. Thus the "total" goes in the denominator, and the fractional bit goes in the numerator.

It's like asking what fraction of a dollar does one penny represent; You don't say it's 100/1.

Oh wow you're actually right, I'm so stupid sometimes lol
I thought it was asking for a ratio when it's actually asking for a fraction. But anyways, thank you guys so much, I've finally cracked the code

 

[austinoude]

I have the same question, but I got 0.157 which is not an option, what did you get?

 

[Remon]

I have the same question, but I got 0.157 which is not an option, what did you get?

I got the exact same answer, but one of the choices was 0.12, so I assumed the difference was caused by the significant digits or the rounding off that we had to do, and I just picked 0.12 since it was the closest answer

 

[haruspex]

I got the exact same answer, but one of the choices was 0.12, so I assumed the difference was caused by the significant digits or the rounding off that we had to do, and I just picked 0.12 since it was the closest answer

To get a fraction as low as that I find I have to put the inner core radius at 2200 or so. Looks like whoever did the calculation in the book made a typo, maybe 2216 for 1216.

 

[Remon]

To get a fraction as low as that I find I have to put the inner core radius at 2200 or so. Looks like whoever did the calculation in the book made a typo, maybe 2216 for 1216.

I swapped 1216 for 2216 and got ≈ 0.12
So screw it, I'm just going to leave it at 2216 lol
thanks for telling us btw

 

[austinoude]

that can't be right... that would mean that the inner and outer core are the same radius

 

[Remon]

that can't be right... that would mean that the inner and outer core are the same radius

So what if they are? screw it, i spent way too much time on this one question, even if the answer is wrong, I'm just going to get 4/5 at least, I'm happy with that