Question:

A circle is circumscribed a square.  The side length of square is  10 .

                        Quantity A                                       Quantity B

Area between circle and square                                  59

A.   If Quantity A is greater

B.   If Quantity B is greater

C.   If Quantity A and Quantity B are equal

D.   The relationship cannot be determined from given information

Solution :

Area of square = 10 x 10 = 100

Area of circle  =  πr² ,

the radius of circle  = hypotenuse of triangle formed by square

So , radius  = 5 √2

Area of circle = π  x 5√2 x 5√2

                             = 157

Therefore area between circle and square = 157 – 100 = 57 . The Quantity B is greater than Quantity A ,  hence the correct answer is ‘B’.