Solved UPSC CDS/OTA Question
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Q · Mensuration Medium · 45s
18 cylindrical water bottles with height same as that of the radius are emptied into a spherical earthen pot. The bottles fill half of the initially empty earthen pot. Find the ratio of the radius of the cylinder and that of the pot.
TopicMensuration
Question Typemultiple choice
DifficultyMedium
Marking+1 / −0.33
Test Duration30 min
Step-by-Step Solution
The complete worked solution.
Every step explained — no skipped algebra.
Let the height and radius of bottles be r
Volume of all bottles = 18(πr₂*r) = 18πr₃
Let the radius of the pot be P.
Half of the volume of the pot = 2πP₃/3
2πP₃/3 = 18πr₃
πP₃ = 27πr₃
P = 3r
Ratio = 1:3
Final Answer: Option A — 1: 3