They Just Can't Help It, Can They.-Jermy...
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No best answer has yet been selected by abbe89. Once a best answer has been selected, it will be shown here.
For more on marking an answer as the "Best Answer", please visit our FAQ.My answer seems to have gone. yes a sphere.
The same type of answer as what's the largest area a lingth of string can surround - a circle. but the proof is quite hard isnt it?
Bernardino's answer is the other way - the smologyui sponge or whatever it is called is the (one of the) smallest volumes for the largest area