Question

.
A steel wire when bent in the form of a square encloses an area of 121 cm. If the same
wire is bent in the form of a circle, find the area of the circle.
​

Answer 1

Answer:

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Step-by-step explanation:

Side of the square =

area

=

121

=11 cm

Perimeter of the square = 4×side=44 cm

Therefore, length of the wire = 44 cm

We know,

Circumference of the circle = Length of the wire

Therefore, Circumference of the circle = 44 cm

Let the radius of the circle be r cm.

Then, 2πr=44

2×

7

22

×r=44

r=7 cm

Therefore, area of the circle = πr

2

=

7

22

×49=154 cm

2

.

Answer 2

Side of the square =  

area

​  

=  

121

​  

=11 cm

Perimeter of the square = 4×side=44 cm

Therefore, length of the wire = 44 cm

We know,

Circumference of the circle = Length of the wire

Therefore, Circumference of the circle = 44 cm

Let the radius of the circle be r cm.

Then, 2πr=44

2×  

7

22

​  

×r=44

r=7 cm

Therefore, area of the circle = πr  

2

=  

7

22

​  

×49=154 cm  

2

.