Question

A silver wire when bent in the form of a square encloses and area of 121 sq.cm. if the same wire is bent in the form of a circle . find the area of the circle

need urgently

Answer 1

Given : The Silver wire when bent in the form of Square encloses an Area of 121 cm²

Let the Side of the Square formed be : S

We know that Area of a Square is : Side × Side

⇒ S × S = 121

⇒ S² = 11²

⇒ S = 11cm

We know that Perimeter of the Square is given by : 4 × Side of Square

⇒ Perimeter of the Square = 4 × 11cm = 44 cm

⇒ Length of the Silver Wire used to make Square is 44 cm

Now this same wire is bent in the form of a Circle.

⇒ Let the radius of the Circle formed be : r

We know that Circumference of Circle is given by : 2π × radius of Circle

As both Circle and Square are made with same length of wire :

Perimeter of Square = Circumference of Circle

⇒ 2π × r = 44

⇒ πr = 22

⇒ $\frac{22(r)}{7} = 22$

⇒ r = 7cm

We know that Area of Circle is given by : πr²

⇒ Area of the Circle = $\frac{22}{7}\times7^2 = 22\times7 = 154 cm^2$

Answer 2

Hey friend here is your answer......

Solution :

Let "α" be the side of the square

Area of the square = 121 sq.cm. (given)

${a}^{2} = 121 = >a \: = 11cm \: (11 \times 11 = 121)$

Perimeter of the square = 4a units

$= 4 \times 11 \: cm$

$44 \: cm$

Length of the wire = Perimeter of the square

$= 44 \: cm$

The wire is bent in the form of a circle

The circumference of the circle = Length of the wire

Therefore, circumference of a circle = 44 cm

$2\pi r = 44$

$2 \times \frac{22}{7} \times r = 44$

$r = \frac{44 \times 7}{44}$

$r = 7 \: cm$

$therefore , \: area \: of \: the \: circle \: = \pi {r}^{2}$
$= \frac{22}{7} \times 7cm \times 7cm$

$area \: of \: the \: circle \: = 154 {cm}^{2}$

Hope it helps you......