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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?Β 

Water is flowing through a cylindrical pipe of internal diameter 2cm

Question 35 - CBSE Class 10 Sample Paper for 2021 Boards - Maths Standard - Part 2
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Question 35 - CBSE Class 10 Sample Paper for 2021 Boards - Maths Standard - Part 4
Question 35 - CBSE Class 10 Sample Paper for 2021 Boards - Maths Standard - Part 5

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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 = π·π‘–π‘Žπ‘šπ‘’π‘‘π‘’π‘Ÿ/2 = 2/2 = 1 cm = 𝟏/𝟏𝟎𝟎 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 Γ— 30 Γ— 60 = 1260 m Thus, Height of cylindrical pipe = 1260 m Now, Volume of water through pipe = Volume of cylinder = πœ‹r2h = πœ‹(1/100)^2 Γ— 1260 = πœ‹ Γ— 1/100 Γ— 1/100 Γ— 1260 = (𝝅 Γ— πŸπŸπŸ”)/𝟏𝟎𝟎𝟎 m3 Volume of tank Tank is in form cylinder where Radius = r = 40 cm = 40/100 m = πŸ’/𝟏𝟎 m Let rise in water level = h m Volume of tank = πœ‹r2h = πœ‹ Γ— (4/10)^2 Γ— h = πŸπŸ”π…π’‰/𝟏𝟎𝟎 m3 Now, Volume of pipe = Volume of tank (𝝅 Γ— πŸπŸπŸ”)/𝟏𝟎𝟎𝟎 = πŸπŸ”π…π’‰/𝟏𝟎𝟎 (πœ‹ Γ— 126)/1000 Γ—100/(16πœ‹ ) = h 126/160 = h β„Ž = 126/160 m β„Ž = 126/160 Γ— 100 cm β„Ž = 1260/16 cm h = 78.75 cm

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.