Thickness of a spherical shell

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BDAndrew

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Hi,

I’m trying to calculate the thickness of a spherical shell, given the radius of that sphere and the volume of the shell.

For context, I am trying to calculate the thickness of a layer within the Moon. The Moons radius is ~1737km, the shell I am calculating has a volume 50% of the mantle which has a radius of ~1400km. So the volume of the mantle is the volume of the Moon minus the volume of the core, and the volume of the layer is the volume of the mantle/2 - but how do I get it’s thickness?

Thank you so much
 
Hello. The moon's core consists of a solid, inner core surrounded by a liquid layer. Between the liquid core and the mantle lies a partially-molten layer. When you refer to the moon's "core", are you including all three layers beneath the mantle or something else?

How did you determine the mantle's radius of 1400km? NASA reports that the moon's crust thickness is about only 70 kilometers on the near-side hemisphere and 150 kilometers on the far-side hemisphere.

Do you know the formula for a sphere's volume (in terms of its radius)? Please share any work that you've already tried. If you're working with a sketch, please upload it. Thank you!

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mmm4444bot said:
Hello. The moon's core consists of a solid, inner core surrounded by a liquid layer. Between the liquid core and the mantle lies a partially-molten layer. When you refer to the moon's "core", are you including all three layers beneath the mantle or something else?

How did you determine the mantle's radius of 1400km? NASA reports that the moon's crust thickness is about only 70 kilometers on the near-side hemisphere and 150 kilometers on the far-side hemisphere.

Do you know the formula for a sphere's volume (in terms of its radius)? Please share any work that you've already tried. If you're working with a sketch, please upload it. Thank you!

Posting Guidelines (Summary)

Welcome to our tutoring boards! :) This page summarizes main points from our posting guidelines. As our name implies, we provide math help (primarily to students with homework). We do not generally post immediate answers or step-by-step solutions. We don't do your homework. We prefer to help...
www.freemathhelp.com
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Hi,

I am working with a paper about the Moons fractionated interior. The paper splits the Moons mantle into 11 layers going down 1400km to the core. Layer ‘0’ is the bottom 50%, followed by 10 equal volume 5% layers above.

Thanks again
 
BDAndrew said:
Hi,

I’m trying to calculate the thickness of a spherical shell, given the radius of that sphere and the volume of the shell.

For context, I am trying to calculate the thickness of a layer within the Moon. The Moons radius is ~1737km, the shell I am calculating has a volume 50% of the mantle which has a radius of ~1400km. So the volume of the mantle is the volume of the Moon minus the volume of the core, and the volume of the layer is the volume of the mantle/2 - but how do I get it’s thickness?

Thank you so much
Click to expand...
If the volume of the mantle with the shell is 1.5 times larger than the volume of the mantle alone what can you tell about the radius ratio ?
 
BDAndrew said:
Hi,

I’m trying to calculate the thickness of a spherical shell, given the radius of that sphere and the volume of the shell.

For context, I am trying to calculate the thickness of a layer within the Moon. The Moons radius is ~1737km, the shell I am calculating has a volume 50% of the mantle which has a radius of ~1400km. So the volume of the mantle is the volume of the Moon minus the volume of the core, and the volume of the layer is the volume of the mantle/2 - but how do I get it’s thickness?

Thank you so much
Click to expand...
Please sketch the "situation" in two dimensions (circles) and post the image of the sketch here. Also label the sketch (different layers).
 
BDAndrew said:
the Moons mantle [has] 11 layers going down 1400km
Click to expand...
Hi BD. In your op, I think you've misused the term 'radius'. The mantle has two radii: the inner radius and the outer radius. The inner radius is the distance from the moon's center to the mantle's nearest boundary; the outer radius is the distance from the moon's center to the mantle's farthest boundary. Your statement above implies that 1400km is the mantle's thickness, not a radius.

However, the distance 1400km seems to include the liquid core layer plus the semi-liquid layer outside it. Those two layers are not part of the mantle. Using approximated distances (in kilometers) of 240 for the solid core, 90 for the liquid core, 150 for the semi-liquid layer and 110 for the crust (i.e., the average of 70 and 150), we have:

1737 – (240 + 90 + 150 + 110) = 1147

Adding back the liquid and semi-liquid layers gets us to close 1400.

1147 + 90 + 150 = 1387

Are you familiar with the volume formula for a sphere? We can use that to calculate the volumes of (1) sphere with the mantle's outer radius and (2) sphere with the inner radius. Subtracting the smaller volume from the larger volume will yield the volume of the mantle. You're looking for half that value.

:)

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Did you finish the problem that you had posted in:

Help rearranging this equation

Hi, I've been given an equation to find out how much water partitions into a solid, but I can't rearrange it? Thanks! Co = Cl*F+Cs*(1-F) I need to find 'Cs' Thanks again
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The process of solving that problem might be useful in solving this problem.
 
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