A rectangular tank measuring 20 cm by 15 cm by 12 cm is 1/4 filled with water. What is the volume of water needed to fill the tank to the brim?
The volume of the tank is given by the formula length * width * height.
So, the volume of the tank is 20 cm * 15 cm * 12 cm = <<20*15*12=3600>>3600 cm³.
If the tank is 1/4 filled with water, then the volume of water in the tank is 1/4 * 3600 = 900 cm³.
To fill the tank to the brim, we need to add water until the tank is full, which means we need to add a volume of 3600 cm³ - 900 cm³ = <<3600-900=2700>>2700 cm³ of water. Answer: \boxed{2700}.