 Visualizing The Area of a Circle Using Rectangles - Maple Help

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Visualizing the Area of a Circle using Rectangles

 Main Concept A circle's area can be visualized by a stack of smaller rectangles. Consider a circle inscribed with small inner rings, where each inner ring can be approximated by a rectangle. When stacked on one another, the rectangles assume the shape of a triangle. We use the formula Area = $\frac{1}{2}$ Base × Height, where we approximate the base as equal to the circle's circumference and the the height as equal to the circle's radius. Using Circumference = 2 × $\mathrm{π}$ × Radius, the equation for the circle's area takes the form Area = $\frac{1}{2}$ × 2 $\mathrm{π}$ r × r = $\mathrm{π}$ ${r}^{2}$.  Explore by changing the radius of the outer circle and the number of inner circles. In this example, the area as computed by summing the individual areas of the stacked rectangles is shown. You will notice that regardless of the two variables, the area computed by this approximation will be extremely close to the circle's actual area. Radius                               : Number of Inner Circles    : More MathApps