Ex 13.3, 9 - A farmer connects a pipe of diameter 20 cm - Ex 13.3

  1. Chapter 13 Class 10 Surface Areas and Volumes
  2. Serial order wise
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Ex 13.3, 9 A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank in her field, which is 10 m in diameter and 2 m deep. If water flows through the pipe at the rate of 3 km/h, in how much time will the tank be filled? Let length of pipe for filling whole tank be h m. So, Volume of pipe = Volume of tank Volume of pipe Pipe is in form of cylinder where Let Height = h m Diameter = 20 cm So, radius = ๐‘‘๐‘–๐‘Ž๐‘š๐‘’๐‘ก๐‘’๐‘Ÿ/2 = 20/2 = 10 cm = 10 ร— 1/100 m = 1/10 m Volume of pipe = Volume of cylinder = ๐œ‹r2h = ๐œ‹(1/10)^2 h = ๐œ‹ ร— 1/100 ร— h = ๐œ‹โ„Ž/100 Volume of tank Tank is in form cylinder where Diameter = 10 m Radius = r = 10/2 m = 5 m Height = h = 2 m Volume of tank = ๐œ‹r2h = ๐œ‹(5)^2 ร— 2 = ๐œ‹ ร— 25 ร— 2 = 50๐œ‹ Now, Volume of pipe = Volume of tank ๐œ‹โ„Ž/100 = 50๐œ‹ h = (50๐œ‹ ร—100 )/๐œ‹ h = 5000 m h = 5 km Now, Water in pipe flows at rate 3 km/hr So, 3 km travels in pipe in = 1 hour 1 km travels in pipe in = 1/3 hr 5 km travels in pipe in = 5/3 hr = 5/3 ร— 60 minutes = 5 ร— 20 minutes = 100 minutes. So, in 100 minutes, the tank will be filled

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