An open box with a rectangular base is to be made from a piece of tin measuring $30$ cm by $40$ cm by cutting out a square from each corner and turning up the sides. Find the dimensions that yield the maximum volume.

$($ I need all steps included and I need you to write with "words" how to slove it$,$ plus the math work. Also make sure the answer is idenifiablle$)$ thank you and please read my requermments