Question

A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank in his field , which is 10 m in diameter and 2m deep. If water flows through the pipe at the rate of 3km /h , in how much time will the tank be filled.​

Answer 1

Answer:

Step-by-step explanation:

r=10 cm

R=500cm

h=200cm

volume of water flows in 1 hr =pie×10×10×300000(cmcube)

volume of cylindrical tank =pie×500×500×200

time taken to be fill the tank=volume of cylindrical tank÷volume of water flow in 1 hr

=(pie×500×500×200)÷pie×10×10×300000

=(5÷3)hr

=(5÷3)×60

=100min

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Answer 2

Let, 

R be the radius and H be the height of the cylinder tank 


Then, 
R = 10/2 m = 5m. and 

H = 2m


Volume of cylinderical tank = π R²H

= π( 5 ) ² ( 2 ) m³ = 50π m³



Let, 
r be the radius of the cross - section of the pipe . Then, 

r = 20/ 2 cm = 10 cm = 1/ 10 m


Now, 

volume of water flowing through the pipe in one hour =

[ π { 1 / 10 } { 1 / 10 } ( 3000 ) ] m³

= 30π m³ ( 3 km = 3000 m )



Now required time = Volume of the tank / Volume of water flowing through the pipe in one hour 

= 50 π / 30 π


= 5 / 3 hr 

= 1 hour 40 minutes.