radinan measure~~

用戶154261

2007-01-11 10:05 pm

the sector OAB is one-quarter of a circle with a radius of 8cm. C is the mid - point of OA in which a semicircle ODA is drawn with C as its centre. A line CDE, which is perpendicular to OA, is drawn at C. find the shaded area.

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回答 (1)

用戶82648

2007-01-11 10:26 pm

✔ 最佳答案

cos∠COE = 4/8 = 0.5
∠COE = π/3
∠COD = π/6
the area of sector OBE = 1/2 (8)^2 (π/3) = 32π/3
the area of ΔOCE = 1/2 (8)(4) sin(π/3) = 8√3
the shaded area = 32π/3 + 8√3 - 1/4 x π(4)^2
　　　　　　　 = 20π/3 + 8√3

2007-01-11 14:30:10 補充：
樓上的這裡錯了Area of ECA= Area of sector AOE - Area of △ COE= 324π/3 - (8)(4)/2 【From (1)】8並非高我開頭以為係高但睇真d先發覺錯左

2007-01-11 15:06:50 補充：
cos∠COE = 4/8 = 0.5∠COE = π/3∠COD = π/6the area of sector OBE = 1/2 (8)^2 (π/6) = 16π/3the area of ΔOCE = 1/2 (8)(4) sin(π/3) = 8√3the shaded area = 16π/3 + 8√3 - 1/4 x π(4)^2　　　　　　　 = 4π/3 + 8√3

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