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Now, imagine peeling more and more strips of width r from our circle, and laying them all out as rectangles side by side, as shown
Now, imagine peeling more and more strips of width r from our circle, and laying them all out as rectangles side by side, as shown in (Figure 3) - starting with the first (outermost) strip at the far right. As you peel more and more, the strips get shorter and shorter because the circle is getting smaller and smaller, until you have the smallest strip laid at far left - this strip, if r is really tiny, is essentially the center of the circle! What is the area of the circle? You've now chopped it into little strips, but notice that the area of the circle is the same as the sum of the areas of all our strips. If r is really small, you can see that all the strips approximate a triangle in the figure Part C (the area under the diagonal line). So the sum of the areas of all our strips is the area of this triangle. What is the area of the triangle? Express your answer in terms of and R
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