Question

a wire is bent in the form of square of area 1936 centimetres sqaure..if the same wire is bent to form a circle.find the radius of the circle and the area enclosed???

Answer 1

area of square=1936
(side)^2=1936
side = 44cm
perimeter of square=4×side
=4×44
=176cm
circumference of circle = perimeter of square
2×22/7×r=176
r=176×7/2×22
r=28cm
area enclosed by circle = 22/7×28×28
=2464cm^2

Answer 2

Answer:

→ Radius of the circle = 28 cm .

→ Area enclosed by the wire = 2464 cm² .

Step-by-step explanation:

First we need to find the length of the wire.

To do that, we should try to figure out the length of 1 side of the square

∵ Area of a square = ( side )² .  

⇒ 1936 cm² = side² .

⇒ side = √( 1936 cm² ) .

∴ side = 44 cm .

Therefore one side of the square would be  44 cm .

→ The Perimeter of the square would be equal to the full length of the wire.

∵ Perimeter of a square = 4 × side .

= 4 × 44 .

= 176 cm .  

→ Therefore the length of the wire would be  176 cm .

∵ If we make a circle from this wire, the length of the wire would then be the Circumference of the Circle .

∵ Circumference of a Circle  = 2πr .

⇒ 176  = 2 × 22/7 ×r .

$\sf \implies r = \frac{176 \times 7}{2 \times 22 } . \\ \\ \huge \boxed { \pink{ \sf \therefore r ( radius ) = 28 cm . }}$  

And,

∵ Area enclose by wire = πr² .

= 22/7 × 28 × 28 .

= 2464 cm² .

Hence, it is solved .

THANKS .