Property, Plant and Equipment, Net - Property, Plant and Equipment, Net (Detail) - USD ($) $ in Millions	Aug. 31, 2022	Aug. 31, 2021
Property, Plant and Equipment [Line Items]
Property plant and equipment	$ 1,241.9	$ 1,226.3
Accumulated depreciation	(596.7)	(556.1)
Property, plant and equipment, net	645.2	670.2
Land and improvements
Property, Plant and Equipment [Line Items]
Property plant and equipment	88.4	94.6
Machinery and Equipment
Property, Plant and Equipment [Line Items]
Property plant and equipment	623.7	609.8
Building and improvements
Property, Plant and Equipment [Line Items]
Property plant and equipment	367.1	379.1
Construction in Progress
Property, Plant and Equipment [Line Items]
Property plant and equipment	55.3	50.0
Other
Property, Plant and Equipment [Line Items]
Property plant and equipment	$ 107.4	$ 92.8