Question 9 - Converting one shape to another - Chapter 12 Class 10 Surface Areas and Volumes

Last updated at May 26, 2023 by Teachoo

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Question 9
A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank in her field, which is 10 m in diameter and 2 m deep. If water flows through the pipe at the rate of 3 km/h, in how much time will the tank be filled?
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 = 20 cm
So, radius = 𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟/2 = 20/2 = 10 cm = 10 × 1/100 m = 1/10 m
Volume of pipe = Volume of cylinder
= 𝜋r2h
= 𝜋(1/10)^2 h
= 𝜋 × 1/100 × h
= 𝜋ℎ/100
Volume of tank
Tank is in form cylinder where
Diameter = 10 m
Radius = r = 10/2 m = 5 m
Height = h = 2 m
Volume of tank = 𝜋r2h
= 𝜋(5)^2 × 2
= 𝜋 × 25 × 2
= 50𝜋
Now,
Volume of pipe = Volume of tank
𝜋ℎ/100 = 50𝜋
h = (50𝜋 ×100 )/𝜋
h = 5000 m
h = 5 km
Now,
Water in pipe flows at rate 3 km/hr
So, 3 km travels in pipe in = 1 hour
1 km travels in pipe in = 1/3 hr
5 km travels in pipe in = 5/3 hr
= 5/3 × 60 minutes
= 5 × 20 minutes
= 100 minutes.
So, in 100 minutes, the tank will be filled

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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