The Sydney Opera House roof shells are derived from a sphere with a radius of about 75 metres—more precisely, 75.2 metres.
This spherical geometry was the breakthrough that made Jørn Utzon's complex roof design practical to construct. Earlier concepts explored parabolas, circular ribs and ellipsoids, but the spherical solution allowed curved components to be produced from a common geometric system. Precast concrete ribs and panels could then be assembled into the distinctive shells.
The shells are not thin concrete domes in the ordinary sense. They are made from precast concrete sections supported by ribs, and their surfaces are covered with more than one million small tiles in glossy white and matte cream. The repeated spherical curvature helped engineers manage the roof's many changing forms while avoiding completely unique formwork for every section.
The stored answer, 75 metres, is a normal rounded rendering of the published 75.2-metre radius. It should not be confused with the shells' height, span or the Opera House's overall dimensions.