Ghost of Guldinus

Geometry Level 4

A solid circumsphere encloses a Reuleaux triangle spheroform hollow void that contains its own solid insphere. If the solid insphere that fills the hollow void has an unit inradius of one find the proportion of the solid mass total the solid insphere will constitute.

Provide your answer as an integer percentage.

Note: The radii of the largest inscribed circle of a Reuleaux triangle of width "s", and of the circumscribed circle of the same triangle, are 0.42265 s & 0.57735 s respectively.

The volume formula of a Reuleaux triangle spheroform of width "s" = 0.44946 s^3.


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