Minimum Area

Move the slider and observe the graph. 

This is a Java Applet created using GeoGebra from www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com

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 .


Download GGB File


Source:

 Abraham Gadalla

"Minimum Area between a Semicircle and a Rectangle"
 http://demonstrations.wolfram.com/MinimumAreaBetweenASemicircleAndARectangle/
 Wolfram Demonstrations Project
 Published: July 1, 2011