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Mass, Volume, Density work with a Sphere

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
 

haruspex

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find the maximum of that function of "a"
According to the equation, if you increase a what happens to m?
 
According to the equation, if you increase a what happens to m?
uhm, if a increases it looks like m will get smaller, right?
 
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...
 

jbriggs444

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jbriggs444

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So if you want to maximize m, what must you do with a?
 
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.
 

jbriggs444

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Yup. There you go.
 
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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