Semi-sphere, based on the fact that there isn't a universally held name right now, a quasphere, if you want to be that sort of guy who corrects everyone on rediit.
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a sphere is called a sphere because , well , its just a other name for a ball such as the earth.
half-sphere hemisphere
The reason a spherometer is called a spherometer is because it measures the radius of a sphere.
Sphere
hemisphere