## 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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