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Ex 13.3, 9 - A farmer connects a pipe of diameter 20 cm - Conversion of one shape to another

Ex 13.3, 9 - Chapter 13 Class 10 Surface Areas and Volumes - Part 2
Ex 13.3, 9 - Chapter 13 Class 10 Surface Areas and Volumes - Part 3
Ex 13.3, 9 - Chapter 13 Class 10 Surface Areas and Volumes - Part 4

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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 = 𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟/2 = 20/2 = 10 cm = 10 × 1/100 m = 1/10 m Volume of pipe = Volume of cylinder = 𝜋r2h = 𝜋(1/10)^2 h = 𝜋 × 1/100 × h = 𝜋ℎ/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 = 𝜋r2h = 𝜋(5)^2 × 2 = 𝜋 × 25 × 2 = 50𝜋 Now, Volume of pipe = Volume of tank 𝜋ℎ/100 = 50𝜋 h = (50𝜋 ×100 )/𝜋 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 × 60 minutes = 5 × 20 minutes = 100 minutes. So, in 100 minutes, the tank will be filled

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.