A wire when bent in the form of a square encloses an area of 484cm2. If the same wire is bent into the form of a circle, find the area of the circle. - Mathematics

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Sum

A wire when bent in the form of a square encloses an area of 484cm2. If the same wire is bent into the form of a circle, find the area of the circle.

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Solution

The side of a square whose area is 484cm2
= `sqrt(484)`
= 22cm
⇒ The perimeter of the square = 4 x 22cm
The Circumference of a Circle with radius r = 2πr
Here, 
2πr = 4 x 22cm

⇒ r = `(88)/(2pi)`

= `(88 xx 7)/(2 xx 22)`
= 14cm
The Area of a Circle with radius r = πr2
The Area of a Circle with radius 14 = π(14)2

= `(22)/(7) xx (14)^2`
= 22 x 2 x 14
= 616cm2.

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Chapter 24: Perimeter and Area - Exercise 24.3

APPEARS IN

Frank Class 9 Maths ICSE
Chapter 24 Perimeter and Area
Exercise 24.3 | Q 22

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