maths! maths! maths!

meilk豆腐貓

2009-08-16 6:33 am

p. 49
Give the answer in terms of [///] if necessary.
1. Find the area of the shaded region in each of the following figures.
a] : http://www.flickr.com/photos/29635386@N06/3823425394/

b] : http://www.flickr.com/photos/29635386@N06/3823425438/

p. 42
A surveyor wants to measure the width of a river. He marks two points A and B on opposite sides of the river and then a point C 20 m from point B along the riverbank. If angle ABC =90度 and angle BCA =68度12’ , how wide is the river?
Figure: http://www.flickr.com/photos/29635386@N06/3822619517/

回答 (1)

用戶9112

2009-08-16 7:20 am

✔ 最佳答案

(1a) Radius of outer circle = 6 + 9 = 15cm
Area of a complete outer circle = π(15)2 = 225π
Area of a complete inner circle = π(9)2 = 81π
Area of a complete ring = 225π – 81π = 144π
Area of shaded part = 144π * 60/360 = 24π
(1b) The shaded area consists of 2 hemispheres and a half ring.
Area of one hemisphere = π(9)2/2
Area of both hemispheres = π(9)2/2 * 2 = 81π
Outer diameter of the half ring = 56 + 18 + 18 = 92
Outer radius = 92/2 = 46
Inner radius = 56/2 = 28
Area of the half ring = (1/2)[π(46)2 - π(28)2]
= (π/2)(2116 – 784)
= 666π
Area of shaded part = 666π + 81π = 747π

68 degrees 12 minutes = 68 + 12/60 = 68.2 degrees
The width of the river is given by 20 * tan68.2 = 50m

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