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Question 21 (OR 1 st question)

Water is flowing at the rate of 15 km per hour through a pipe of diameter 14cm into a rectangular tank which is 50 m long and 44 m wide. Find the time in which the level of water in the tank will rise by 21 cm.

Water is flowing at the rate of 15 km per hour through a pipe of

Question 21 (Or 1st) - CBSE Class 10 Sample Paper for 2019 Boards - Part 2
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Question 21 (OR 1st question) Water is flowing at the rate of 15 km per hour through a pipe of diameter 14cm into a rectangular tank which is 50 m long and 44 m wide. Find the time in which the level of water in the tank will rise by 21 cm. 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 = 14 cm So, radius = π·π‘–π‘Žπ‘šπ‘’π‘‘π‘’π‘Ÿ/2 = 14/2 = 7 cm = 7/100 m Volume of pipe = Volume of cylinder = πœ‹r2h = πœ‹(7/100)^2 h = 22/7 Γ— 7/100 Γ— 7/100 Γ— h = (22 Γ— 7)/10000h Volume of tank Tank is in form cuboid where Length = l = 50 m Breadth = b = 44 m Height = h = 21 cm = 21/100 m Volume of tank = lbh = 50 Γ— 44 Γ— 21/100 = (44\ Γ— 21)/2 = 22 Γ— 21 Now, Volume of pipe = Volume of tank (22 Γ— 7)/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 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 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.