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
CBSE Class 10 Sample Paper for 2021 Boards - Maths Standard
CBSE Class 10 Sample Paper for 2021 Boards - Maths Standard
Last updated at July 19, 2026 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 = š·ššššš”šš/2 = 2/2 = 1 cm = š/ššš 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 Ć 30 Ć 60 = 1260 m Thus, Height of cylindrical pipe = 1260 m Now, Volume of water through pipe = Volume of cylinder = šr2h = š(1/100)^2 Ć 1260 = š Ć 1/100 Ć 1/100 Ć 1260 = (š Ć ššš)/šššš m3 Volume of tank Tank is in form cylinder where Radius = r = 40 cm = 40/100 m = š/šš m Let rise in water level = h m Volume of tank = šr2h = š Ć (4/10)^2 Ć h = ššš š/ššš m3 Now, Volume of pipe = Volume of tank (š Ć ššš)/šššš = ššš š/ššš (š Ć 126)/1000 Ć100/(16š ) = h 126/160 = h ā = 126/160 m ā = 126/160 Ć 100 cm ā = 1260/16 cm h = 78.75 cm