Given a circle, a circumscribed square is one that completely encloses the circle, and an inscribed square is one that is completely enclosed by the circle, as shown below:

If the the difference in the areas of the two squares is 35 sq. m., then what is the area of the circle? (Assume π =  
22
7
 )


Answer:

55 sq. m.

Step by Step Explanation:
  1. Let's name the outer square as ABCD, and the inner square as PQRS as shown below:
  2. If the radius of the circle is R, the side of the outer square will be double of circle's radius:
    AB = 2R
  3. Area of outer square,
    Area(ABCD) = 2R × 2R = 4R2
  4. Side of the inner square PQRS can be calculated using Pythagoras Theorem:
    PQ = ^@ \sqrt {R^2 + R^2} ^@
    or, PQ = √2R
  5. Area of inner square,
    Area(PQRS) = √2R × √2R = 2R2
  6. The difference in areas of the two squares is given to be 35 sq. m.
    Thus, Area(ABCD) - Area(PQRS) = 35
    ⇒ 4R2 - 2R2 = 35
    ⇒ 2R2 = 35
    ⇒ R2 =  
    35
    2
     
  7. Now that we know the radius of the circle, we can calculate the area of the circle using the formula,
    Area(circle) = πR2
    =  
    22
    7
      ×  
    35
    2
     
    = 55 sq. m.

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