CREATE TABLE table_37683 ("Name" TEXT, "Status" TEXT, "Population" FLOAT, "District" TEXT, "Former local authority" TEXT)

What district is the parish who had the South Cambridgeshire rural district as the former local authority?
SELECT "District" FROM table_37683 WHERE "Former local authority" = 'south cambridgeshire rural district'
SELECT "District" FROM "table_37683" WHERE "Former local authority" = 'south cambridgeshire rural district'