Question

A wire can be bent in the form of a circle of radius 56 cm. If it is bent in the form fo a square, then its area will be

Options

• 3520 cm²

• 6400 cm²

• 7744 cm²
  
  

• 8800 cm²

Answer 1

We have given that a wire is bent in the form of circle of radius 56 cm. If we bent the same wire in the form of square of side a cm, the perimeter of the wire will not change.

∴ perimeter of the circle = perimeter of the square

`∴ 2pi r=4a`

We know that r = 56 cm.

Now we will substitute the value of r in the equation,

`2xxpixx56=4a`............(1)

`∴ 2xx22/7xx56=4a`

`∴2xx22xx8=4a`

Dividing both sides of the equation by 4 we get,

`∴ a=(2xx22xx8)/4`

`∴ a=2xx22xx2` 

`∴ a=88`

Now we obtained side of the square. Now we can calculate the area of the square as given below.

Area of the square=`a^2`

Area of the square=`88 ^2`

Area of the square=`7744`

Hence, the area of the square is `7744 cm^2`