Approximating the area of semi-circle

As we showed in class, the area of a semi-circle can be approximated by creating a sum of “rectangle approximations.”  In class we used rectangles with a “delta-x” (width of rectangle) equal to 1 unit.  Below is the same calculation using a width of .5 units.  This calculation shows an area of 156.423 square units which is closer to the actual area of 157.080 square units, an error of .418%.

Similarly, it can be show that working with rectangle widths of .1 unit, the area approximation method gives a total area of 157.021 square units, which represents an error of only .038%.

area of semi circle by pt 5 (1)

 

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About mrsiderer

I am am a mechanical engineer and a math and physics teacher. I like to understand the way things work, to know about new things that are being developed, and to understand how math impacts everything. I value my time and yours and will only post quality material.
This entry was posted in calculus how to do it, Worked out Calculus problems and tagged . Bookmark the permalink.

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