overflow:none will keep it from flowing out of its boundaries. if you need set a height that way it will stop at the end of the height.
If you want to add a lot more text but you want t box to be a certain size in height then go ahead and add overflow:auto this will keep the box the same size but create a scroll bar on the left and right. you can hide or show these by scroll bars by leaving them alone and by default they will show or hide them by overflow-y:hidden; or overflow-x:hidden;
Also you might create a border all the way around this box and make the color of the borders on the sides you have not declared one to blend in to your back round. this will also help keep the text in its area.