Jenny divides a particular circle into some identical sectors. She finds that 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?
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2009-08-17 7:25 pm
回答 (1)
2009-08-18 7:18 am
✔ 最佳答案
It also depends on the unit of measurement. Suppose the unit of measurement are cm and cm2.Circumference of a circle = 2πr
Area of a circle = πr2
Suppose the sector is 1/n of a complete circle,
Arc length = 2πr (1/n)
Area of section = πr2 (1/n)
Arc length = Area of section =>
2πr (1/n) = πr2 (1/n)
r = 2 cm
The condition is that the radius of the circle must be 2 (with respect to the unit of measurement used).
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