Question 21 (Or 1st) - CBSE Class 10 Sample Paper for 2019 Boards - Solutions of Sample Papers for Class 10 Boards

Last updated at Sept. 24, 2021 by Teachoo

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.

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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·πππππ‘ππ/2 = 14/2 = 7 cm
= 7/100 m
Volume of pipe = Volume of cylinder
= πr2h
= π(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

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.