Armor against 8-inch cruiser fire

How much armor does a heavy cruiser need against 8-inch gunfire?

It depends on range, but roughly eight inches is the suggested protection level.

Protection depends first on the range at which the cruiser is expected to fight. Armor cannot be specified sensibly without the velocity and angle at which shells will arrive. About eight inches offers a broad design estimate against 8-inch fire. The engagement envelope, rather than calibre alone, is the starting point for an armor scheme.