What is are the dimensions of a cylinder inside a sphere with a radius of 30cm so that the area of the cylinder is a maximum?

[Hedgehogofchaos]

What is are the dimensions of a cylinder inside a sphere with a radius of 30cm so that the area of the cylinder is a maximum?

The radius of the sphere is 30cm just to clarify.

 

[auser]

Calculus to the rescue!
See these:

http://answers.yahoo.com/question/index?qid=20091202122213AAnFNOp

http://mathforum.org/library/drmath/view/53525.html

http://www.algebra.com/algebra/homework/Volume/Volume.faq.question.192419.html

 

[DeathStrudel]

Learn to do calculus!

h = √1200
r = √600

 

[DeathStrudel]

umm....where is says ̾ those are supposed to be square root signs, but they apparently didn't show up

 

[Hedgehogofchaos]

I understand how to do everything but the initial setting up o the equation to obtain a value for "r".

I don't understand this conclusion
h² + (2r)² = (diameter of sphere)²

The diameter would equal 2r would it not?

 

[Hedgehogofchaos]

As well we are not Allowed to use trig.

 

[DeathStrudel]

The radius of the cylinder is different from the radius of the sphere so the diameter of the sphere is NOT 2r. And i'm pretty sure you can't do this problem without using the Pythagorean theorem

 

[mechadylan]

h² + (2 X radius of cylinder)² = (diameter of sphere)²

Hope this helps.

 

[Fishaman P]

Dude, you have to do your own homework.

 

[alex_0706]

yeah why do we need to do your homework

 

[ATMB]

I just remember that the volume of a sphere inscribed in a cylinder is 2/3 of the volume of the cylinder...

 

[Snailface]

Both the height and diameter of the cylinder with the maximum volume* are 2(450^.5) or 42.4264cm.

*You meant volume, right? Or did you need surface area?

 

[Snailface]

I worked the problem again and got a different answer. This should be right:

Cylinder height: sqr rt of 1200 or 34.641 cm
Radius: sqr rt of 600 or 24.4949 cm
(for max volume)

 

[CraddaPoosta]

I desperately hope you fail this class. You should immediately get off the computer, find your mother and father, slap the hell out of them for failing you as providers, parents and guides, and actually pay attention in school.

I am literally nauseous.

 

[Advi]

do your own damn homework

P.S. http://www.wolframalpha.com/

 

[Deboog]

Here I made a thing for you. For some reason the image isn't showing up. Click the link.

EDIT oh this was from BEFORE AskGbaTemp went down in 2011. Oh well better late then never.