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?
Last updated at Oct. 27, 2020 by Teachoo
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 = ๐ท๐๐๐๐๐ก๐๐/2 = 2/2 = 1 cm = ๐/๐๐๐ 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 = ๐r2h = ๐(1/100)^2 ร 1260 = ๐ ร 1/100 ร 1/100 ร 1260 = (๐ ร ๐๐๐)/๐๐๐๐ m3 Volume of tank Tank is in form cylinder where Radius = r = 40 cm = 40/100 m = ๐/๐๐ m Let rise in water level = h m Volume of tank = ๐r2h = ๐ ร (4/10)^2 ร h = ๐๐๐ ๐/๐๐๐ m3 Now, Volume of pipe = Volume of tank (๐ ร ๐๐๐)/๐๐๐๐ = ๐๐๐ ๐/๐๐๐ (๐ ร 126)/1000 ร100/(16๐ ) = h 126/160 = h โ = 126/160 m โ = 126/160 ร 100 cm โ = 1260/16 cm h = 78.75 cm
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CBSE Class 10 Sample Paper for 2021 Boards - Maths Standard
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