Question

A wire when bent in the form of a square, encloses an area of 121 cm². The same wire is bent in the form of a circle. Find the area enclosed by the circle.

Answer 1

Given: A wire bent as a square encloses area = 121 cm². The same wire is rebent as a circle; find the circle’s area.

Step-wise calculation:

1. Side of square

= `sqrt(121)`

= 11 cm

2. Perimeter (length of wire)

= 4 × 11

= 44 cm

3. Circumference of circle

= 44

= 2πr

Using π = `22/7`: 

`2 xx 22/7 xx r = 44` 

⇒ r = 7 cm

4. Area of circle

= πr² 

= `22/7 xx 7^2` 

= `22/7 xx 49` 

= 154 cm²

The area enclosed by the circle is 154 cm².