Area of a Circle

Being in the piping trade and the fact that pipes are round, one of the things we have to teach our students about is area of a circle. In school we are taught the area of a circle is:

πr2

But where does this formula come from? I always just accepted this was the formula, but I was asked this by a student recently and I didn't have an answer for him.

I went on my computer and found this video that does a great job of explaining the formula. After I showed the video to my class I found that once they understood where the formula came form using the formula became a lot easier for them.