# 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"?

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Is there any other
equation between a and m If you can tell me then I can help you

haruspex
Homework Helper
Gold Member
2020 Award
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
Homework Helper
uhm, if a increases it looks like m will get smaller, right?
Right. And if you decrease a?

Right. And if you decrease a?

Then m would get larger.

jbriggs444
Homework Helper
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