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The following figure consists of a square, inside which there is a second square formed by joining the midpoints of the sides of the outer square. Inside the second square is inscribed a circle, and it continues in a similar manner. Find the ratio of the sum of areas of all the squares combined to the sum of the areas of the circles combined.
  • a)
    12/π
  • b)
    18/π
  • c)
    16/π
  • d)
    9/π
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
The following figure consists of a square, inside which there is a sec...
Let the length of each side of the outermost square be a.
Hence, the length of each side of the second square = 
The radius of circle = length of side of square / 2 = 
Let the side of the square inside the circle be b.

Hence, b =a/2
Similarly, the side of the square inner to this square = 
Similarly radius of the inner circle = 
And it continues.
Hence, the sum of areas of the squares =  ...

Hence, ratio = 
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