Question

prove the area of circle is πr^2

Answer 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.