GATE ME 2022 Set 2 — Question 10
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General Aptitude → Quantitative Aptitude → Mensuration & Geometry
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Question
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.
What is the ratio of the areas of unshaded regions of case M to that of case N?
Correct answer
(B) 1: 1
Solution
The area of the unshaded region is calculated as: .Case M: The square has a side of 1 cm. It contains 4 equal circles. The diameter of each circle is cm, so the radius cm.
Total shaded area in M = .
Unshaded area in M = .Case N: The square has a side of 1 cm. It contains 9 equal circles. The diameter of each circle is cm, so the radius cm.
Total shaded area in N = .
Unshaded area in N = .Since the unshaded areas are identical, the ratio is .
Total shaded area in M = .
Unshaded area in M = .Case N: The square has a side of 1 cm. It contains 9 equal circles. The diameter of each circle is cm, so the radius cm.
Total shaded area in N = .
Unshaded area in N = .Since the unshaded areas are identical, the ratio is .
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