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Water is flowing at the rate of 15 km/h through a pipe of diameter 14 cm into a cuboidal pond which is 50 m long and 44 m wide. In what time will the level of water in pond rise by 21 cm? What should be the speed of water if the rise in water level is to be attained in 1 hour

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Let length of pipe for filling whole pond be h m. So, Volume of pipe = Volume of cuboidal pond Volume of pipe Pipe is in form of cylinder where Let Height = h m Diameter = 14 cm So, Radius = π·π‘–π‘Žπ‘šπ‘’π‘‘π‘’π‘Ÿ/2 = 14/2 = 7 cm = πŸ•/𝟏𝟎𝟎 m Volume of pipe = Volume of cylinder = πœ‹r2h = 𝝅(πŸ•/𝟏𝟎𝟎)^𝟐 h = 22/7 Γ— 7/100 Γ— 7/100 Γ— h = (𝟐𝟐 Γ— πŸ•)/𝟏𝟎𝟎𝟎𝟎 h Volume of cuboidal pond Pond is in form cuboid where Length = l = 50 m Breadth = b = 44 m Height = h = 21 cm = 𝟐𝟏/𝟏𝟎𝟎 m Volume of pond = lbh = 50 Γ— 44 Γ— 𝟐𝟏/𝟏𝟎𝟎 = (44\ Γ— 21)/2 = 22 Γ— 21 Now, Volume of pipe = Volume of pond (𝟐𝟐 Γ— πŸ•)/𝟏𝟎𝟎𝟎𝟎h = 22 Γ— 21 h = (22 Γ— 21 Γ— 10000)/(22 Γ— 7) h = 30,000 m h = 30 km Now, Water in pipe flows at rate 15 km/hr So, 15 km travels in pipe in = 1 hour 1 km travels in pipe in = 1/15 hour 30 km travels in pipe in = 30/15 hour = 2 hours So, in 2 hours, the pond will be filled We also need to find the speed of water if the rise in water level is to be attained in 1 hour. We know that Pond takes 2 hours to attain rise at given speed = 15 km/h If it wants to fill in 1 hour, it’s speed should be double Therefore, Speed of water required to attain rise in 1 hour = 15 Γ— 2 = 30 km/h

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.