Visualizing The Area of a Circle Using Sectors - Maple Help

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Visualizing the Area of a Circle using Sectors

Main Concept

Consider a circle being divided into pie slices, or sectors. The circle's area can be easily visualized by rearranging these sectors to form a rectangle. We use the formula Area = Length x Width, and approximate the length of the rectangle to be half of the circumference, where the circumference is given by 2πRadius. Combining these two formulae, the area is given by  πrr = πr2. Although we use only approximations for the length and width, the resulting formula for the circle's area is exact.

Explore by changing the number of sectors, using the slider. You will notice that as the number of sectors increases, the shape of the rearranged components will resemble that of a rectangle more closely. In this method, one of the sectors is halved for better rearrangement. Note that the number of sectors can only be even.

Number of Sectors:  

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