DECLARE @temp table ([name] varchar(10), [geom] geography);
INSERT INTO @temp values ('Point', geography::STGeomFromText('POINT(-122.34900 47.65100)', 4326));
INSERT INTO @temp values ('LineString', geography::STGeomFromText('LINESTRING(-122.360 47.656, -122.343 47.656)', 4326));
INSERT INTO @temp values ('Polygon', geography::STGeomFromText('POLYGON((-122.358 47.653, -122.348 47.649, -122.348 47.658, -122.358 47.658, -122.358 47.653))', 4326));
SELECT [name], [geom].STDimension() as [dim]
FROM @temp;