Question

A metal wire, when bent in the form of a square of largest area, encloses an area of 484 cm square. Find the length of the wire. If the same wire is bent to a larger circle, find:
(i) radius of the circle formed.
(ii) area of the circle.

Answer 1

Area of the square =484 cm2

So each of its sides will be a=14√area=22cm

So its perimeter =4×22==88cm

The circle formed by bending the same wire will have same perimeter 88cm. If the circle has got radius r then

2πr=88

⇒r=882π=88×72×22=14cm

So the area enclosed by the circle =πr2=227×142=616cm2

Answer 2

Answer:

Area of square={side}^{2}

side=√484

=22cm

Perimeter of square=4×side

=22×4

=88cm

Circumference of circle=Perimeter of square=88

Circumference=2πr

=2×(22/7)×r

r=(88×7)/(2×22)

=14cm

Area of circle=π×{r}^{2}

={14}^{2}×(22/7)

=616cm^2