Math, asked by Anonymous, 1 year ago


Prove that the area of circle is πr² when r is the radius.

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Answers

Answered by Anonymous
1
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
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Anonymous: this is the shortest method! well with integration....... thank u:)
Answered by sourishdgreat1
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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