for a given volume, which shape has the least surface area?

Question

muzzack · Answer

where is the given volume

arabpride · Answer

and i assume there are also images o the shapes. c: lease include them too

anonymous · Answer

no dnt assume anything :)
lets the volume be X :)

anonymous · Answer

its a nice question :)

asnaseer · Answer

I believe its a sphere - see here: http://en.wikipedia.org/wiki/Sphere Snippet from that wen page: "The sphere has the smallest surface area of all surfaces that enclose a given volume, and it encloses the largest volume among all closed surfaces with a given surface area. The sphere therefore appears in nature: for example, bubbles and small water drops are roughly spherical because the surface tension locally minimizes surface area."

anonymous · Answer

cool , but why ?
whats the mathmatical value about it ?

asnaseer · Answer

it's an optimisation problem - something that "nature" has solved :)

anonymous · Answer

ok , but its pure math also :P

asnaseer · Answer

Sure - you can see some hints at how this might be solved mathematically here: https://answers.yahoo.com/question/index?qid=20071019213552AANdb52

asnaseer · Answer

I found one proof, but it is by no means /simple/ - it is better known as the isoperimetric inequality: http://math.stanford.edu/~jbooher/expos/isoperimetric_promys.pdf