Qubik of Orb
Using parallel planes, we want to cut up the unit radius sphere into multiple regions, where the ratio of the surface area to volume is a constant across the regions, and the total composite surface area exceeds the magnitude of the unit radius sphere's initial value.
What is the minimum number of regions?
The answer is 3.
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1 solution
Diameter = D = 2
Height of Cap(s) = H = 0.74589
Total Area of "3" Regions of equal surface area-to-volume ratio = Pi x [ D ^2 + 8 x H - ( 4 x H ^2 ) ] >= 24