A wire, when bent in the form of a square encloses an area of 196cm². If the same wire is bent in form of a circle, find the area?

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Solution

First we need to find the length of the wire.

For that,

Let "a" be the side of a square.

So,area of the square=a^2 =196.

Therefore,

a = √196 = 16 cm

So, length of the wire = 16 × 4 =64 cm
(because square had 4 sides)

Since, the same wire is used to make a circle,perimetre of the circle = 64 cm.

But perimetre of a circle = 2πr .

so , we get

2πr = 64

so radius ,r = 64/(2π) = 64/(2×3.14) = 64/6.28 =10.19 cm.

Therefore,area of the circle = π ×r^2 = 3.14×10.19^2 = 326.04cm^2.

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A wire, when bent in the form of a square encloses an area of 196cm2 . If the same wire is bent in form of a circle, find the area?

A wire, when bent in the form of a square encloses an area of 196cm². If the same wire is bent in form of a circle, find the area?