HKIMO 2017 THPT (Grades 10–12 shared) National Final (Heat) Set 04 Question 20

A rectangular container measures $18$ cm by $15$ cm by $12$ cm high. Water is initially $7$ cm deep. A cube of side $9$ cm is put inside. By how many cm does the water level rise?

Editorial working convention: The solid cube rests flat on the bottom and absorbs no water.