RS Aggarwal - Mathematics

Book: RS Aggarwal - Mathematics

Chapter: 18. Area of Circle, Sector and Segment

Subject: Maths - Class 10th

Q. No. 44 of Exercise 18A

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44

A wire is bent to form a square enclosing an area of 484 m2. Using the same wire, a circle is formed. Find the area of the circle.

Given:

Perimeter of square = Circumference of circle ………………. (i)


Area of Square = 484m2


Let the side of square be ‘x’ cm.


Area of Square = side × side


484 = x × x


x2 = 484


x = √484 = 22cm


Perimeter of square = 4 × side


= 4 × 22 = 88 cm


Using (i), we have


Circumference of circle = 88 cm


Also, Circumference of Circle = 2πr


2πr = 88


2 × × r = 88


r = 88 × ×


r = 2 × 7 = 14 cm


Area of Circle = πr2 = × 14 × 14


= 22 × 2 × 14 = 616 cm2


Hence, the area of Circle is 616 cm2.


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