Question 35 - CBSE Class 10 Sample Paper for 2021 Boards - Maths Standard - Solutions of Sample Papers for Class 10 Boards
Last updated at Oct. 27, 2020 by Teachoo
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·πππππ‘ππ/2 = 2/2 = 1 cm
= π/πππ 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
= πr2h
= π(1/100)^2 Γ 1260
= π Γ 1/100 Γ 1/100 Γ 1260
= (π Γ πππ)/ππππ m3
Volume of tank
Tank is in form cylinder where
Radius = r = 40 cm
= 40/100 m = π/ππ m
Let rise in water level = h m
Volume of tank = πr2h
= π Γ (4/10)^2 Γ h
= πππ π/πππ m3
Now,
Volume of pipe = Volume of tank
(π Γ πππ)/ππππ = πππ π/πππ
(π Γ 126)/1000 Γ100/(16π ) = h
126/160 = h
β = 126/160 m
β = 126/160 Γ 100 cm
β = 1260/16 cm
h = 78.75 cm
Made by
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.
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