Question 35 - CBSE Class 10 Sample Paper for 2021 Boards - Maths Standard - Solutions of Sample Papers for Class 10 Boards
Last updated at May 29, 2023 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?
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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 = 𝐷𝑖𝑎𝑚𝑒𝑡𝑒𝑟/2 = 2/2 = 1 cm
= 𝟏/𝟏𝟎𝟎 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 × 30 × 60
= 1260 m
Thus,
Height of cylindrical pipe = 1260 m
Now,
Volume of water through pipe = Volume of cylinder
= 𝜋r2h
= 𝜋(1/100)^2 × 1260
= 𝜋 × 1/100 × 1/100 × 1260
= (𝝅 × 𝟏𝟐𝟔)/𝟏𝟎𝟎𝟎 m3
Volume of tank
Tank is in form cylinder where
Radius = r = 40 cm
= 40/100 m = 𝟒/𝟏𝟎 m
Let rise in water level = h m
Volume of tank = 𝜋r2h
= 𝜋 × (4/10)^2 × h
= 𝟏𝟔𝝅𝒉/𝟏𝟎𝟎 m3
Now,
Volume of pipe = Volume of tank
(𝝅 × 𝟏𝟐𝟔)/𝟏𝟎𝟎𝟎 = 𝟏𝟔𝝅𝒉/𝟏𝟎𝟎
(𝜋 × 126)/1000 ×100/(16𝜋 ) = h
126/160 = h
ℎ = 126/160 m
ℎ = 126/160 × 100 cm
ℎ = 1260/16 cm
h = 78.75 cm
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.
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