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Equal sized circular regions are shaded in a square sheet of paper of 1 cm side length. Two cases, case M and case N, are considered as shown in the figures below. In the case M, four circles are shaded in the square sheet and in the case N, nine circles are shaded in the square sheet as shown.

Q. What is the ratio of the areas of unshaded regions of case M to that of case N?
  • a)
    2 : 3
  • b)
    1 : 1
  • c)
    3 : 2
  • d)
    2 : 1
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
Equal sized circular regions are shaded in a square sheet of paper of ...
Case M :

Diameter of a shaded circle = 1/2 cm
Radius of shaded circle = 1/4 cm
Area = π/16 cm
2

So, Area of unshaded region = Area of square sheet – Area of 4 shaded circular region.
∴ Area of unshaded region

Case N :

diameter = 1/3 and radius = 1/6
∴ Area of unshaded region of case N = Area of square sheet – Area of shaded circular region.

∴ The ratio of the areas of unshaded region of case M to that of case N

= 1:1
Hence, the correct option is (B).​​​​​​​​​​​​​​
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Equal sized circular regions are shaded in a square sheet of paper of 1 cm side length. Two cases, case M and case N, are considered as shown in the figures below. In the case M, four circles are shaded in the square sheet and in the case N, nine circles are shaded in the square sheet as shown.Q. What is the ratio of the areas of unshaded regions of case M to that of case N?a)2 : 3b)1 : 1c)3 : 2d)2 : 1Correct answer is option 'B'. Can you explain this answer?
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