The contact cement is a bad idea to glue pieces of plywood together. Instead, utilize a waterproof glue for plywood that often has exposure to water and humidity - for instance, the Titebond ii for the interior projects and the Titebond iii for the exterior one. Suppose you need to avoid the plywood from becoming deteriorated or rotted; waterproof it. You can use one combo of sealant and oil or simply silicone caulk.