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maths

用戶3519

2008-07-28 7:42 am

1.Try to draw a line segment with the length of √26 cm using right angled triangle and Pythagoras theorem.

2.Jenny divides a particular circle into some identical sectors.She finds no matter how she divides the circle,the value of the area of each sector is always equal to the value of the arc length of each sector .Do you think it is possible?Explain your answer briefly. If it is possible, What is the condition of the circle?

回答 (1)

用戶10012

2008-07-28 3:48 pm

✔ 最佳答案

Q.1
Draw a line AB with 5 unit length. Draw another line AC which is perpendicular to AB with 1 unit length. Length of BC will be sqrt26.
By Pythagoras theorem, BC^2 = AB^2 + AC^2
BC^2 = 5^2 + 1^2 = 25 + 1 =26. Therefore BC = sqrt26.
Q.2
Arc length = 2(pi)r x n/360, where n is the angle of the sector.
Area of sector = (pi)r^2 x n/360.
If they are numerically equal, that means
2(pi)r x n/360 = (pi)r^2 x n/360
that is r = 2.
Therefore, value of area of sector is always equal to the value of arc length NUMERICALLY if radius of circle is 2. No matter what is the value of the angle n.

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