A wire can be bent in the form of a circle of radius 56 cm.

Question:

A wire can be bent in the form of a circle of radius 56 cm. If it is bent in the form fo a square, then its area will be

(a) $3520 \mathrm{~cm}^{2}$

(b) $6400 \mathrm{~cm}^{2}$

(c) $7744 \mathrm{~cm}^{2}$

(d) $8800 \mathrm{~cm}^{2}$

Solution:

We have given that a wire is bent in the form of circle of radius 56 cm. If we bent the same wire in the form of square of side a cm, the perimeter of the wire will not change.

$\therefore$ perimeter of the circle $=$ perimeter of the square

$\therefore 2 \pi r=4 a$

We know that r = 56 cm.

Now we will substitute the value of r in the equation,

$2 \times \pi \times 56=4 a$.......(1)

$\therefore 2 \times \frac{22}{7} \times 56=4 a$

$\therefore 2 \times 22 \times 8=4 a$

Dividing both sides of the equation by 4 we get,

$a=\frac{2 \times 22 \times 8}{4}$

$\therefore a=2 \times 22 \times 2$

$\therefore a=88$

Now we obtained side of the square. Now we can calculate the area of the square as given below.

Area of the square $=a^{2}$

$\therefore$ Area of the square $=88^{2}$

$\therefore$ Area of the square $=7744$

Hence, the area of the square is $7744 \mathrm{~cm}^{2}$.

Therefore, the correct answer is $(c)$.

 

 

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