Prove that the area of circle is πr² when r is the radius.
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let at a distance x dx width element is selected
Area of dx element = 2piex dx
integration from 0 to r , 2 pie x dx
2 pie x^2/2
pie x^2
put x= r
pie r^2
Area of dx element = 2piex dx
integration from 0 to r , 2 pie x dx
2 pie x^2/2
pie x^2
put x= r
pie r^2
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Anonymous:
this is the shortest method! well with integration....... thank u:)
Answered by
1
Consider a circle divided into large number of sectors as shown Cut the sectors and arrange them as shown so that it forms a rectangle Length of rectangle = half the circumference of the circle = 2Пr/2= Пr Breadth of the rectangle = r (radius of the circle) Area of rectangle = length x breadth = πr x r = πr2 Hence area of a circle is πr2 sq units.
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