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Mass, Volume, Density work with a Sphere

  1. May 31, 2015 #1
    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. jcsd
  3. May 31, 2015 #2
    Is there any other
    equation between a and m If you can tell me then I can help you
  4. May 31, 2015 #3


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    According to the equation, if you increase a what happens to m?
  5. May 31, 2015 #4
    uhm, if a increases it looks like m will get smaller, right?
  6. May 31, 2015 #5
    No other equation that is given to me. I think we have to formulate our own...
  7. May 31, 2015 #6


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    Right. And if you decrease a?
  8. May 31, 2015 #7
    Then m would get larger.
  9. May 31, 2015 #8


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    So if you want to maximize m, what must you do with a?
  10. May 31, 2015 #9
    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.
  11. May 31, 2015 #10


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    Yup. There you go.
  12. May 31, 2015 #11
    You are awesome, I love how you did that for me! Incredible!
    Thank you, jbriggs444!
  13. May 31, 2015 #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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