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?Ā 

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
Question 35 - CBSE Class 10 Sample Paper for 2021 Boards - Maths Standard - Part 3 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

Remove Ads

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 = š·š‘–š‘Žš‘šš‘’š‘”š‘’š‘Ÿ/2 = 2/2 = 1 cm = šŸ/šŸšŸŽš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 Ɨ 30 Ɨ 60 = 1260 m Thus, Height of cylindrical pipe = 1260 m Now, Volume of water through pipe = Volume of cylinder = šœ‹r2h = šœ‹(1/100)^2 Ɨ 1260 = šœ‹ Ɨ 1/100 Ɨ 1/100 Ɨ 1260 = (š… Ɨ šŸšŸšŸ”)/šŸšŸŽšŸŽšŸŽ m3 Volume of tank Tank is in form cylinder where Radius = r = 40 cm = 40/100 m = šŸ’/šŸšŸŽ m Let rise in water level = h m Volume of tank = šœ‹r2h = šœ‹ Ɨ (4/10)^2 Ɨ h = šŸšŸ”š…š’‰/šŸšŸŽšŸŽ m3 Now, Volume of pipe = Volume of tank (š… Ɨ šŸšŸšŸ”)/šŸšŸŽšŸŽšŸŽ = šŸšŸ”š…š’‰/šŸšŸŽšŸŽ (šœ‹ Ɨ 126)/1000 Ɨ100/(16šœ‹ ) = h 126/160 = h ā„Ž = 126/160 m ā„Ž = 126/160 Ɨ 100 cm ā„Ž = 1260/16 cm h = 78.75 cm

Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh is an IIT Kanpur graduate and has been teaching for 16+ years. At Teachoo, he breaks down Maths, Science and Computer Science into simple steps so students understand concepts deeply and score with confidence.

Many students prefer Teachoo Black for a smooth, ad-free learning experience.