Question

A wire when bent in the form of a square encloses an area of 484 sq. Cm. Of the same wire is bent in the form of a circle, what is the area enclosed by it

Answer 1

Explanation:

area of squre= 484 cm^2

a^2= 484 cm^2

a^2= 22×22 cm^2

a= 22cm

because square is made by wire and circle also made by same wire ,so

perimeter of square = circumference of circle

4a = 2 Pi r

4(22) = 2 pi r

4(22)/2×pi = r {pi =22/7}

4×22×7/22

14 cm = r

now, area of circle = pi r^2

= pi(14)^2

=22/7×14×14

=22×2×14

=308×2 cm^2

=616 cm^2

Answer 2

Let each side of a square be x cm and radius of the circle be r cm

Area of the square = $\sf{{484cm}^{2}}$

$\therefore$ $\sf{ {x}^{2} = 484 = x = 22cm}$

$\therefore$ Perimeter of the square

= 22 × 4 = 88cm = Length of the wire

= Circumference of the circle, when the same wire is bent in the form of a circle

= 2πr = 88

= $\sf{r=\frac{44}{π}}$

$\therefore$ Area of the circle =

= $\sf{\pi \times \frac{44}{\pi} \times \frac{44}{\pi} = \frac{44}{22} \times 7 \times 44}$

= $\sf{ {616cm}^{2}}$