a maths一問 - Ans.fyi 參考答案

a maths一問

Mandy

2007-12-14 5:19 am

Two wheels of radii 17cm and 8cm are surrounded tightly by a belt.The distance betweeno and o', he centers of the two wheels , is 41cm.
a) Find the length of the belt.
b)Find the area enclosed by the belt.
(correct your ans. to 2 decimal places.)

http://img139.imageshack.us/my.php?image=aabbwy9.png

ans:a) 162.52cm
b) 1604.28cm^2

explain how to do it!!

回答 (2)

用戶82648

2007-12-14 6:22 am

✔ 最佳答案

Let α be the angle between OO' and the radius of O' in your diagram
β係細圓touch到條belt個sector既angle

(a)
cosα = (17 - 8)/41
α = 1.349481 rad
β = 2α = 2.698962 rad
the length of the belt touch in smaller circle = (8)(2.69862) = 21.58896 cm
the length of the belt touch in larger circle = (17)(2π - 2.698964) = 60.93174 cm
the length of the belt in straight part = 2 x √(41² - 9²) = 80 cm
The length of the belt = 21.58896 + 60.93174 + 80 = 162.52070 cm = 162.52 cm

(b)
Area
= ½ (8)(21.58896) + ½ (17)(60.93174) + 2[(17 + 8)40/2]
= 1604.28 cm²

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CHANMING

2008-12-28 10:36 pm

Why β = 2α?

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