作业帮[求解]已知面积求半径的一道数学题
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[求解]已知面积求半径的一道数学题
In this following diagram,each of the three intersecting circles has the same radius,and the center point of each circle is at the intersection of the other two circles.The blue shaded region has an area of exactly 2010 square centimetres.
见下图：三个圆半径相同,并且每个圆的圆心都与其他两个圆相切,已知蓝色部分面积为2010平方厘米,求圆的半径,四舍五入到小数点第二位.
In this following diagram,each of the three intersecting circles has the same radius,and the center point of each circle is at the intersection of the other two circles.The blue shaded region has an area of exactly 2010 square centimetres.
见下图：三个圆半径相同,并且每个圆的圆心都与其他两个圆相切,已知蓝色部分面积为2010平方厘米,求圆的半径,四舍五入到小数点第二位.
原图蓝色部分面积是4个紫色三角形面积与6个红色面积之和.而红色部分面积是扇形面积（紫+红）与紫色三角面积之差.因此,原图蓝色部分面积=紫*4+（扇形面积-紫）*6=扇形面积*6-紫*2=圆面积-紫*2设圆的半径为R2010=πR*R-1/2*R*(√3/2)R*2计算解得R=29.72