Q27 of 35 Page 311

If the perimeter of a circular field was decreased by 50%, let us write by calculating what per cent it decreases the area of circular field.

Let the radius of the circular field be r units.


Circumference = 2π r


The area of a circle = πr2


Now, decreasing the perimeter to 50%



New perimeter =3πr


⇒ New radius = 1.5r


Area of new circle = π(1.5r)2


⇒ Area of new circle = 2.25πr2


Increase in area =2.25πr2 - πr2 =1.25πr2


Per centage increase in the area of circular field


⇒ Percentage increase = 125%


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