Trinity

Geometry Level 4

A unit radius sphere split into three uniform spherical wedges (regular trigonal hosohedron) all have an area to volume ratio of \(A\). The same unit radius sphere partitioned into 3 solid sections by 2 parallel planes with both spherical caps (calotte) each having a height of 0.7458904 units all have an area to volume ratio of \(B\). If \(A = B - 0.7458904^2 \), find \(A\) to 2 decimal places.

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