Question

A steel wire when bent in the form of a square encloses an area of 121 cm 2 . If the same wire is bent in the form of a circle, find the area of
the circle.

Answer 1

Answer:

Let a cm be the side of square. Then area of square is

a²=121

⇒

a=11cm

Now, length of the wire = Perimeter of the square = 4a = 44 cm

Let the radius of the circle be r. Then,

Circumference of circle = Length of wire

⇒

2πr=44

2×22/7×r=44

⇒

r=7cm

Now, we will calculate area of the circle as

πr2=22/7×7×7

=

154cm²

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× 22/7 × r = 44

r=7cm

Therefore, area of the circle = πr² = 22/7 ×49=154cm ²