CBSE Class 10 Sample Paper for 2021 Boards - Maths Standard

Class 10
Solutions of Sample Papers for Class 10 Boards

## 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?Β

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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 = π·πππππ‘ππ/2 = 2/2 = 1 cm = π/πππ 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 Γ 30 Γ 60 = 1260 m Thus, Height of cylindrical pipe = 1260 m Now, Volume of water through pipe = Volume of cylinder = πr2h = π(1/100)^2 Γ 1260 = π Γ 1/100 Γ 1/100 Γ 1260 = (π Γ πππ)/ππππ m3 Volume of tank Tank is in form cylinder where Radius = r = 40 cm = 40/100 m = π/ππ m Let rise in water level = h m Volume of tank = πr2h = π Γ (4/10)^2 Γ h = ππππ/πππ m3 Now, Volume of pipe = Volume of tank (π Γ πππ)/ππππ = ππππ/πππ (π Γ 126)/1000 Γ100/(16π ) = h 126/160 = h β = 126/160 m β = 126/160 Γ 100 cm β = 1260/16 cm h = 78.75 cm