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Volume help,

  1. May 6, 2009 #1
    1. The problem statement, all variables and given/known data

    A closed cylinder has total surface area equal to [tex] 600\pi [/tex].

    Show that the volume, Vcm3, of this cylinder is given by the formula[tex] v = 300\pi-\pi r^3 [/tex],
    where r cm is the radius of the cylinder.
    Find the maximum volume of such a cylinder.



    2. Relevant equations

    [tex] V= 2\pir^2 + 2\pirh [/tex]

    3. The attempt at a solution

    not really sure where to start,

    [tex] 600\pi = 2\pir^2 + 2\pirh [/tex]

    how would I make this expression equal the other?

    Thanks!
     
  2. jcsd
  3. May 6, 2009 #2

    HallsofIvy

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    A, the total surface area, is [itex]2\pi r^2+ 2\pi rh[/itex], not the volume.

    Yes, that is correct.

    Well, first you have to decide what the "other" expression is! What is the formula for volume of a cylinder? And you don't "make them equal". Solve the equation giving surface area for h and use that to replace h in the formula giving volume.

     
  4. May 6, 2009 #3
    Latex gone horribly wrong.

    this is the question;

    A closed cylinder has total surface area equal to 600π. Show that the volume, Vcm3, of this cylinder is given by the formula V=300πr−πr3, where r cm is the radius of the cylinder.
    Find the maximum volume of such a cylinder

    n=pi
     
  5. May 6, 2009 #4
    well the formula for the volume of a cylinder = v= 2\pir^2 + 2\pirh so if I set that equal to 600\pi, what do I do after that?
     
  6. May 6, 2009 #5

    so If I solve for 'h' from 600\pi = 2\pir^2 + 2\pirh I get; 300-r^2/r = h,

    600\pi = 2\pir^2 + 2\pi(300-r^2)/r -----that does not simplify to the desired expression, what did I do wrong?
     
    Last edited: May 6, 2009
  7. May 7, 2009 #6
    Actually h=(300-r^2)/r not 300-r^2/r

    I don't even know which formula you are trying to substitute the h in. You need to put the h in the general formula for the area of a any cylinder.
     
  8. May 8, 2009 #7

    HallsofIvy

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    It looks like you have solve the area equation for h in terms of r and the replace h in the area equation! You want to replace h in the volume equation so as to get a formula for volume in terms of r only. The volume of a cylinder, of base radius r and height h, is [itex]V= \pi r^2 h[/itex].
     
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