Question

A wire 22 centimetre long it is bent to form a square and the same wire is bent to form a circle. By how much the area of circle exceeds by the area of square?​

Answer 1

Solution :

The length of the wire = 22 cm

If a square be made from the wire, then the square's each side's length be

  = 22 / 4 cm = 5.5 cm

So, its area (A) = 5.5² cm² = 30.25 cm²

Let, the radius of the made circle be r cm

Then, its perimeter = 2πr cm

By the given condition,

  2πr = 22

  or, 2 * (22 / 7) * r = 22

  or, r = 7 / 2

  or, r = 3.5

So, circle's radius = 3.5 cm

Thus, its area be

  B = πr² cm²

     = 22 / 7 * 3.5² cm²

     = 22 / 7 * 12.25 cm²

     = 38.5 cm²

Hence, the area of the circle exceeds the area of the square by

  = (B - A) cm², since B > A

  = (38.5 - 30.25) cm²

  = 8.25 cm²

Answer 2

Solution :-

Given :-

Length of the Wire = 22 cm.

For Square,

Sides of the Square = 22 / 4

=> Side of the Square = 5.5 cm

Now,

Area of Square = Side²

=> Area = 5.5 * 5.5 = 30.25 cm²

For Circle,

Circumference of the Circle = 22 cm ( Since, The same Wire is used to form a Circle. So, Circumference will be same.)

=> 2 πr = 22

=> 2 * 22/7 * r = 22

=> r = (22 * 7)/22*2

=> r = 3.5 cm.

Now, Area of Circle = π r²

=> 22/7 * 3.5 * 3.5

=> Area of Circle = 38.5 cm²

Now,

Difference between the area of Square & Circle .

=> Area of Circle - Area of Square

=> 38.5 cm² - 30.25 cm²

=> 8.25 cm²

Hence,

By 8.25 cm² the Area of Circle exceeds by the Area of Square.