Question 249955
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A circle with a diameter of 10 has a radius of 5.  The area of a circle is the radius squared times *[tex \Large \pi].  5 squared is 25, and since *[tex \Large \pi] is more than 3, the area has to be more than 3 times 25 = 75 and since *[tex \Large \pi] is less than 4, the area has to be smaller than 4 times 25 = 100.  But a square has an area that is the measure of the side squared.  10 squared is 100.  So which has a larger area?


Another way to look at it is this.  If a square measures 10 on a side, then it also measures 10 across the center.  So if you take a circle with a diameter of 10 and put it on top of the square so their centers coincide, the circle would just fit.  But the circle wouldn't cover the entire square - you would have those 4 sort-of triangle shaped pieces in the corners that weren't covered.



John
*[tex \LARGE e^{i\pi} + 1 = 0]
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