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.
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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.
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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:
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