Question

A copper wire when bent in the form of a square encloses an area of 121 CM square if the same wire is bent in the form of a circle then find the area of the circle​

Answer 1

Here is your answer.

area of square :-

$121 = {l}^{2} \\ l = \sqrt{121} = 11cm$

perimeter = 4 × l = 4 × 11 = 44cm

perimeter = circumference

$circumference = 2.\pi.r \\ 44 = 2 \times \frac{22}{7} \times r \\ \frac{44 \times 7}{44} = r \\ r = 7cm$

area of circle :-

$= \pi {r}^{2} \\ = \frac{22}{7} \times 7 \times 7 \\ = 54 {cm}^{2}$

area of circle is 54{cm}^{2}

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Answer 2

Answer:

Step-by-step explanation:

So are of square = 121 cm^2

Now formula of area of square = a^2. (Where a is the side of the square)

So, side of the square

=> a^2 = 121

Square root on both the sides. We get,

=> a = 11cm

So as the length of the copper wire is the same for the square and the circle.

4a = 2 pi (r). (Formula for the perimeter of the square and the circle)

So,

4(11) = 2 pi (r)

44 = 2 pi (r)

22 = pi (r)

22 * 7/22 = r. (As value of pi is 22/7)

So,

7cm = r

So,

Area of circle = pi (r)^2

So,

(22/7) * 7 * 7

=> 22 * 7

=> 154cm^2

So the area of the circle is 154cm^2

Hope it helps:)