Question

A wire when bent in the form of a square, encloses an area of 196 m². If the same wire is bent to form a circle, find the area of the circle.​

Answer 1

Aиѕωєr —

• Area of circle = 249.45 cm²

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Giνєи Qυєѕтiσи —

A wire when bent in the form of a square, encloses an area of 196 m². If the same wire is bent to form a circle, find the area of the circle.

Hєrє, we have :

• Area of square = 196 cm²

We know that :

➤ Area of square = ( side ) ²

➤ 196 cm² = ( side ) ²

➤ side = √ 196

➤ side = 14 cm

Tнєrєfσrє —

• Perimeter of square :

➤ Perimeter = 4 × side

➤ Perimeter = 4 × 14

➤ Perimeter = 56 cm

i.e , length of wire is 56 cm .

➙ Circumference of circle is 56 cm .

➤ circumference = 2πr

➤ 56 = 2πr

➤ 56 = 2 × 22/7 × r

➤ r = ( 56 × 7 ) / ( 2 × 22 )

➤ r = 98 / 11 cm

Tнєrєfσrє —

• Area of circle :

➤ Area = πr²

➤ Area = ( 22 / 7 ) × ( 98 / 11 ) × ( 98 / 11 )

➤ Area = ( 22 × 98 × 98 ) / ( 7 × 11 × 11 )

➤ Area = ( 211288 ) / ( 847 )

➤ Area = 249.54

❝ Hence , the area of circle is 249.45 cm² ❞