Question

A steel wire when bent in the form of a square encloses an area of 121 cm² . The same wire is bent in the form of a circle. Find the area of the circle. ​

Answer 1

Step-by-step explanation:

Area of square =(side)²

121=side².

√121=side.

Side=11cm.

Perimeter of square = length of steel wire.

=> 4×side => 4×11 => 44cm.

Also, Perimeter of square = circumference of circle.

=> 44=2×22/7×r.

=> 44×7/2×22=r

=> r=7.

Area of circle=πr².

=> 22/7×7²

=> 22×7

=> 154cm².

Answer 2

Given :-

A steel wire when bent in the form of a square encloses an area of 121 cm²

The same wire is bent in the form of a circle.

To Find :-

The area of the circle.

Solution :-

We know that,

• a = Area
• r = Radius
• d = Diameter

Given that,

Area of the square (a) = 121 cm²

By the formula,

$\underline{\boxed{\sf Area \ of \ circle= \pi r^{2}}}$

$\underline{\boxed{\sf Area \ of \ square=2 \times Side}}$

Substituting them,

121 cm² = a²

So, a = 11 cm

Thus,

Each side of the square = 11 cm

Now,

$\underline{\boxed{\sf Perimeter \ of \ square = 4a }}$

By substituting,

$\sf = 4 \times 11 = 44 \ cm$

According to the question,

Perimeter of the square = Circumference of the circle

We know,

$\underline{\boxed{\sf Circumference \ of \ circle=2 \pi r}}$

Now, further

$\sf 4a = 2 \pi r$

$\sf 44=2\dfrac{22}{7} r$

$\sf r=7 \ cm$

Next,

$\underline{\boxed{\sf Area \ of \ circle=\pi r^{2}}}$

Substituting their values,

$\sf =\dfrac{22}{7} \times 7 \times 7$

$\sf =154 \ cm^{2}$

Therefore, the area of the circle is 154 cm²