aaaaaa1234 said:
i need help doing this, i can't figure it out. and there are too many circles.
Here's another approach...start with some MUCH SIMPLER problems, and see if you can see a pattern that will lead you to a result for the complex problem.
What if there are just TWO circles....radius 1 for the smaller one, and radius 2 for the larger. What's the area between the two circles?
area of big circle - area of small circle = pi*2[sup:2ll1lhjl]2[/sup:2ll1lhjl] - pi*1[sup:2ll1lhjl]2[/sup:2ll1lhjl] = 4 pi - pi, or 3 pi
What if there are FOUR circles, with radii 1, 2, 3, and 4. You already know that the area between the first two circles is 3 pi. Find the area between the third and fourth circles, and add that to what you already have: 3pi + [pi*4[sup:2ll1lhjl]2[/sup:2ll1lhjl] - pi*3[sup:2ll1lhjl]2[/sup:2ll1lhjl]}, or 3pi + (16 pi - 9 pi), or 3 pi + 7 pi, or 10 pi
With 2 circles, area is 3 pi
With 4 circles, area is 10 pi
Continue this process...