Water is flowing through a cylindrical pipe of internal diameter 2cm, into a cylindrical tank of base radius 40 cm at the rate of 0.7m/sec. By how much will the water rise in the tank in half an hour? 

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  1. Class 10
  2. Solutions of Sample Papers for Class 10 Boards

Transcript

Let Rise in water level be h meters Now, Volume of water through pipe in 30 minutes= Volume of tank Volume of water through pipe in 30 minutes Pipe is in form of cylinder where Diameter = 2 cm So, Radius = ๐ท๐‘–๐‘Ž๐‘š๐‘’๐‘ก๐‘’๐‘Ÿ/2 = 2/2 = 1 cm = ๐Ÿ/๐Ÿ๐ŸŽ๐ŸŽ m Now, Rate of filling water is 0.7 m/sec So, In 1 second, water flowing through pipe = 0.7 m Water flowing through pipe in in 30 minutes = 0.7 ร— 30 ร— 60 = 1260 m Thus, Height of cylindrical pipe = 1260 m Now, Volume of water through pipe = Volume of cylinder = ๐œ‹r2h = ๐œ‹(1/100)^2 ร— 1260 = ๐œ‹ ร— 1/100 ร— 1/100 ร— 1260 = (๐… ร— ๐Ÿ๐Ÿ๐Ÿ”)/๐Ÿ๐ŸŽ๐ŸŽ๐ŸŽ m3 Volume of tank Tank is in form cylinder where Radius = r = 40 cm = 40/100 m = ๐Ÿ’/๐Ÿ๐ŸŽ m Let rise in water level = h m Volume of tank = ๐œ‹r2h = ๐œ‹ ร— (4/10)^2 ร— h = ๐Ÿ๐Ÿ”๐…๐’‰/๐Ÿ๐ŸŽ๐ŸŽ m3 Now, Volume of pipe = Volume of tank (๐… ร— ๐Ÿ๐Ÿ๐Ÿ”)/๐Ÿ๐ŸŽ๐ŸŽ๐ŸŽ = ๐Ÿ๐Ÿ”๐…๐’‰/๐Ÿ๐ŸŽ๐ŸŽ (๐œ‹ ร— 126)/1000 ร—100/(16๐œ‹ ) = h 126/160 = h โ„Ž = 126/160 m โ„Ž = 126/160 ร— 100 cm โ„Ž = 1260/16 cm h = 78.75 cm

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.