Answer :
Answer:
It takes 100 minutes to fill the tank.
Step-by-step explanation:
Let the length of the pipe used for filling the tank be h
Then
Volume of the pipe = volume of the tank
Step 1: Finding the volume of the pipe
The pipe is in cylindrical form with height h and diameter 20m
The volume of the pipe = [tex]\pi r^2h[/tex]
Where r is the radius of the pipe
r = [tex]\frac{diameter}{2}[/tex]
r = [tex]\frac{20}{2}[/tex]
r = 10cm = [tex]\frac{1}{10}[/tex]
The volume of the pipe
=> [tex]\pi (\frac{1}{10})^2 h[/tex]
=> [tex]\frac{1}{100}\pi h[/tex]
=> [tex]\frac{\pi h}{100}[/tex]-----------------------------------(1)
Step 2: Finding the volume of the tank
The volume of the tank = [tex]\pi r^2h[/tex]
Where r is the radius of the tank
r = [tex]\frac{diameter}{2}[/tex]
r = [tex]\frac{10}{2}[/tex]
r = 5
The volume of the pipe
=> [tex](\pi )(5)^2 (2)[/tex]
=> [tex]50 \pi[/tex]-------------------------------------(2)
Equating (1) and (2)
[tex]\frac{\pi h}{100}[/tex] = [tex]50 \pi[/tex]
[tex]\frac{h}{100}[/tex] = 50
h = 50 X 100
h =5000m =5km
The flow rate of water through the pipe = 3 km/hr
time taken to travel 3 km = 1 hours
so time taken 1 km = [tex]\frac{1}{3}[/tex] hours
To Travel 5 km
=> [tex]5 \times \frac{1}{3}[/tex] hours
=> [tex]\frac{5}{3}[/tex] hours
converting into minutes
=> [tex]\frac{5}{3} \times 60[/tex]
=>[tex]\frac{300}{3}[/tex]
=> 100 minutes