radian measure....－oob73zj92b的部落格

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radian measure....

發問:

Two wheels of radii 17cm and 8cm are surrounded tightly by a belt.The distance between O and O' , the centres of the two wheels , is 41cm.(a) Find the length of the belt.(b) Find the area enclosed by the belt(Correct answers to 2 decimal... 顯示更多 Two wheels of radii 17cm and 8cm are surrounded tightly by a belt.The distance between O and O' , the centres of the two wheels , is 41cm. (a) Find the length of the belt. (b) Find the area enclosed by the belt (Correct answers to 2 decimal places.) thx!!! http://i143.photobucket.com/albums/r141/tokomon123/20080822132.jpg

最佳解答:

圖片參考：http://i295.photobucket.com/albums/mm158/Audrey_hepburn2008/A_Hepburn01Aug231441.jpg?t=1219473748 a. Draw O2E, O2E is perpendicular to O1D. O1E = ED - O2C = 17 - 8 = 9 cm CD = O2E = √[412 - 92] = 40 cm ∠O1O2E = cos-1(40/41) ∠O2O1E = cos-1(9/41) ∠BO2C = 2π - π/2 - π/2 - 2cos-1(40/41) = π - 2cos-1(40/41) Length of arc BC = O2B X ∠BO2C = 21.5917 cm Major ∠AO1D = 2π - 2cos-1(9/41) Length of major arc AD = O1D X Major ∠AO1D = 60.9318 cm So, length of the belt = 60.9318 + 21.5917 + 40 + 40 = 162.52 cm (cor. to 2 d.p.) b. Area of tranpezium O1O2CD = Area of O1O2BA = (8 + 17)(40) / 2 = 500 cm2 Area of sector BO2C = 1/2 (8)2(π - 2cos-1(40/41)) = 86.3668 cm2 Area of major sector AO1D = 1/2 (17)2(2π - 2cos-1(9/41)) = 517.92 cm2 Area enclosed by the belt = 517.92 + 500 X 2 + 86.3668 = 1604.28 cm2 (cor. to 2 d.p.)

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