Question

A steel wire when bent in the form of a square encloses an area of 121 cm square. The same wire is bent in the form of a circle. Find the area of the circle.​

Answer 1

✬ Area = 154 cm² ✬

Step-by-step explanation:

Given:

• Area of wire when it is in the form of square is 121 cm².
• Same wire is bent to form a circle.

To Find:

• What is the area of circle ?

Solution: Let the measure of each side of square be x cm.

As we know that

★ Area of Square = Side² ★

A/q

• Area is 121 cm²

➟ x² = 121

➟ x = √121

➟ Side = √11 × 11 = 11 cm.

So each of side of square is of 11 cm.

If we bent the wire in to circle then

• perimeter of square = circumference of circle.

★ Perimeter of Square = 4 × Side ★

➟ Perimeter = 4 × 11 = 44 cm

Now,

★ Circumference of Circle = 2πr ★

➟ 2πr = 44

➟ 2 × 22/7 × r = 44

➟ r = 44 × 7/44

➟ r = 7 cm

Now finding the area of circle

★ Area of Circle = πr² ★

$\implies{\rm }$ 22/7 × 7 × 7

$\implies{\rm }$ 22 × 7

$\implies{\rm }$ 154 cm²

Hence, the area of circle is 154 cm².

Answer 2

SoLuTiOn :

• Here , it is given area of steel wire bent in form of square is 121 cm² .

— Now , $\small \sf Side\: of\: square \:= \: \sqrt {121} \:=\:11\:cm$

$\:\:\:\: \implies \small \sf Perimeter\:of\:Square\:=\:4\: \times\: Side\: \\ \:\:\:\:\:\:\:\:\: \small \sf =\:4\: \times\:11\: \\ \:\:\:\:\:\:\:\:\: \small \sf =\:44\:cm$

• It is given , Same wire is used to make circle , so , the length of wire will be equal to circumference of the circle made .

$\:\:\:\: \implies \small \sf Circumference\:of\:circle\:=\:44\:cm$

• Now , We have to find area of circle but for that we require the radius of circle , Let the radius be r here :

$\implies \small\sf 2πr\:=\:44$

$\implies \small\sf r\:=\: \dfrac{44 \:\times\: 7}{2\: \times\:22}$

$\implies \small{\underline{\sf{\red{ r\:=\:7\:cm}}}}$

• Area Of Circle = $\\ \implies \small \sf πr² \:=\: \dfrac{22}{7}\: \times\:(7)² \:=\: \dfrac{22}{7}\: \times \: 49$

$\implies \large{\boxed{\tt{\red{Area\:of\:circle\:=\:154\:cm²}}}}$

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