Monday, December 19, 2011

Minimum Area

Move the slider and observe the graph. 

This is a Java Applet created using GeoGebra from - it looks like you don't have Java installed, please go to

The figure shows a semicircle of radius one and a horizontal line parallel to the diameter. What central angle corresponds to the minimum shaded area? This problem can be solved by either integration or trigonometry. The shaded area is equal to , where  is the central angle. The minimum shaded area occurs when the central angle is .

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"Minimum Area between a Semicircle and a Rectangle"
 Wolfram Demonstrations Project
 Published: July 1, 2011

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