Question

5. A wire is bent in the form of a square of area 1936 cm2. If the same wire is bent to form a
circle, find the radius of the circle and the area enclosed.
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Answer 1

$\huge\mathbb{Solution:}$

→ 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 .

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

∵ Perimeter of a square = 4 × side .

= 4 × 44 .

= 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 .

.°. Radius = 28cm

And,

∵ Area enclose by wire = πr² .

= 22/7 × 28 × 28 .

= 2464 cm² .

Hence, it is solved .

Answer 2

Answer:

Area of square =1936cm^2

(Side)^2 =1936cm^2

(Side)=44cm

Perimeter of square=4* side

4*44

176cm

Circumference of circle=perimeter of square

2*22/7*r=176

r=28cm

Area enclosed by circle=22/7*28*28

=2464cm^2