Mass, Volume, Density work with a Sphere

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Homework Help Overview

The discussion revolves around a problem involving a spherical shell with varying inner radius and its mass, volume, and density. The original poster seeks to determine the mass of the sphere as a function of the inner radius and explore conditions for maximizing this mass.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the relationship between the inner radius "a" and the mass "m," questioning how changes in "a" affect "m." There is an exploration of whether there are other equations relating "a" and "m." Some participants suggest that decreasing "a" increases "m," while increasing "a" appears to decrease "m."

Discussion Status

The discussion is active, with participants engaging in reasoning about the effects of changing "a" on "m." There is a recognition that to maximize "m," "a" should be minimized, leading to further exploration of the implications of this approach.

Contextual Notes

Participants note that no additional equations are provided, which may limit their exploration of the problem. The focus remains on the implications of the given equation for mass as a function of "a."

jdsconsumer
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A spherical shell has an outside radius of 2.75 cm and an inside radius of a. The shell wall has uniform thickness and is made of a material with density 4.59 g/cm3. The space inside the shell is filled with a liquid having a density of 1.00 g/cm3. (a) Find the mass m of the sphere, including its contents, as a function of a.

Answer that I got much help on from previous helpers: m = 399.33 - 4.79 pi ( a^3 ) grams

(b) For what value of a does m have its maximum possible value?

(c) What is this maximum mass?

(d) Explain whether the value from part (c) agrees with the result of a direct calculation of the mass of a solid sphere of uniform density made of the same material as the shell.

I am now on part (b). So am I trying to find the maximum of that function of "a"?
 
Last edited:
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Is there any other
equation between a and m If you can tell me then I can help you
 
jdsconsumer said:
find the maximum of that function of "a"
According to the equation, if you increase a what happens to m?
 
haruspex said:
According to the equation, if you increase a what happens to m?

uhm, if a increases it looks like m will get smaller, right?
 
ArmanCham said:
Is there any other
equation between a and m If you can tell me then I can help you

No other equation that is given to me. I think we have to formulate our own...
 
jdsconsumer said:
uhm, if a increases it looks like m will get smaller, right?
Right. And if you decrease a?
 
jbriggs444 said:
Right. And if you decrease a?

Then m would get larger.
 
So if you want to maximize m, what must you do with a?
 
jbriggs444 said:
So if you want to maximize m, what must you do with a?

make it smaller and smaller until I can't make it any smaller? So if I reduced it to 0, the minimum it's radius could be, then m couldn't get any larger at that point. At least from the decrement of a.
 
  • #10
Yup. There you go.
 
  • #11
jbriggs444 said:
Yup. There you go.

You are awesome, I love how you did that for me! Incredible!
Thank you, jbriggs444!
 
  • #12
grrr, why was that so hard for me to talk through on my own?! That is awesome! I feel so much better now!
 

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