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Volume help,

  • Thread starter tweety1234
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  • #1
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Homework Statement



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.



Homework Equations



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

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!
 

Answers and Replies

  • #2
HallsofIvy
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Homework Statement



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.



Homework Equations



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

The Attempt at a Solution



not really sure where to start,

[tex] 600\pi = 2\pir^2 + 2\pirh [/tex]
Yes, that is correct.

how would I make this expression equal the other?
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.

Thanks!
 
  • #3
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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
 
  • #4
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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?
 
  • #5
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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.

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:
  • #6
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so If I solve for 'h' from 600\pi = 2\pir^2 + 2\pirh I get; 300-r^2/r = h,
Actually h=(300-r^2)/r not 300-r^2/r

600\pi = 2\pir^2 + 2\pi(300-r^2)/r -----that does not simplify to the desired expression, what did I do wrong?
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.
 
  • #7
HallsofIvy
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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?
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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