Mass, Volume, Density work with a Sphere

[jdsconsumer]

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"?

 

[ArmanCham]

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

 

[haruspex]

find the maximum of that function of "a"

According to the equation, if you increase a what happens to m?

 

[jdsconsumer]

According to the equation, if you increase a what happens to m?

uhm, if a increases it looks like m will get smaller, right?

 

[jdsconsumer]

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]

uhm, if a increases it looks like m will get smaller, right?

Right. And if you decrease a?

 

[jdsconsumer]

Right. And if you decrease a?

Then m would get larger.

 

[jbriggs444]

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

 

[jdsconsumer]

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]

Yup. There you go.

 

[jdsconsumer]

Yup. There you go.

You are awesome, I love how you did that for me! Incredible!
Thank you, jbriggs444!

 

[jdsconsumer]

grrr, why was that so hard for me to talk through on my own?! That is awesome! I feel so much better now!