Question

a copper wire when bent in the form of a square and area of 484 cm^2 enclosed. if the same wire is bent in the form of a circle. find the area of circle enclosed by it.

Answer 1

a^2=484

a = 22 so side of square = 22

perimeter of square = 4 into side = 4 into 22 = 88 cm

so perimeter of circle = 88 cm

2 into 22/7 into r = 88

r=88/2 into 7/22

r=44 into 7/22 = 14 cm

area of circle = 22/7 into 14 into 14

area = 28 into 22 = 616 sq.cm

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 =

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

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