GATE EC 2026 Set 1 — Question 9
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Question
The city of Atlantis was crafted by the God of the seas, Poseidon. It was made of alternating concentric circular rings of land (shaded) and water (not shaded) as represented in the figure (not to scale). The radius of Inner Island was stades (a unit of length used in ancient Greece). The water surrounding Inner Island was one stade wide (length ). This was surrounded by two pairs of alternating rings of land and water. The first pair of land and water was two stades wide each (lengths and ), and the outer pair is three stades wide each (lengths and ).The ratio of the surface area of the land to that of the water in the city of Atlantis is _________ (round off to two decimal places).
Correct answer
(C) 0.75
Solution
Let be the radius of the Inner Island (land). stades.
Width of water ring 1 () = 1 stade. Radius stades.
Width of land ring 1 () = 2 stades. Radius stades.
Width of water ring 2 () = 2 stades. Radius stades.
Width of land ring 2 () = 3 stades. Radius stades.
Width of water ring 3 () = 3 stades. Radius stades.Total Land Area ():
Total Water Area ():
Ratio of Land Area to Water Area:
Ratio Rounding off to two decimal places, the ratio is 0.75.
Width of water ring 1 () = 1 stade. Radius stades.
Width of land ring 1 () = 2 stades. Radius stades.
Width of water ring 2 () = 2 stades. Radius stades.
Width of land ring 2 () = 3 stades. Radius stades.
Width of water ring 3 () = 3 stades. Radius stades.Total Land Area ():
Total Water Area ():
Ratio of Land Area to Water Area:
Ratio Rounding off to two decimal places, the ratio is 0.75.
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