Mass, Volume, Density work with a Sphere

1. May 31, 2015

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"?

Last edited: May 31, 2015
2. May 31, 2015

ArmanCham

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

3. May 31, 2015

haruspex

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

4. May 31, 2015

jdsconsumer

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

5. May 31, 2015

jdsconsumer

No other equation that is given to me. I think we have to formulate our own...

6. May 31, 2015

jbriggs444

Right. And if you decrease a?

7. May 31, 2015

jdsconsumer

Then m would get larger.

8. May 31, 2015

jbriggs444

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

9. May 31, 2015

jdsconsumer

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. May 31, 2015

jbriggs444

Yup. There you go.

11. May 31, 2015

jdsconsumer

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

12. May 31, 2015

jdsconsumer

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