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 · Apr 26, 2011

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 · Apr 26, 2011

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 · Apr 26, 2011

Learn to do calculus!

h = √1200
r = √600

DeathStrudel · Apr 26, 2011

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

Hedgehogofchaos · Apr 26, 2011

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 · Apr 26, 2011

As well we are not Allowed to use trig.

DeathStrudel · Apr 26, 2011

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 · Apr 26, 2011

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

Hope this helps.

Fishaman P · Apr 26, 2011

Dude, you have to do your own homework.

alex_0706 · Apr 26, 2011

yeah why do we need to do your homework

ATMB · Apr 26, 2011

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

Snailface · Apr 27, 2011

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 · Apr 27, 2011

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 · Apr 27, 2011

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 · Apr 28, 2011

do your own damn homework

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

Deboog · Jun 1, 2015

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.

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?

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