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 2 m deep. if water flows through the pipe at the rate of 3km /hr , in how much time will the tank be filled ??

Answer 1

good question,

Hey... Mate here's ur solution

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.


Hope it might be helpful :)

Answer 2

Answer:

Step-by-step explanation:

Consider the following diagram-

ncert solutions for class 10 maths chapter 13 fig 17

ncert solutions for class 10 maths chapter 13 fig 18

Volume of water that flows in t minutes from pipe = t × 0.5π m3

Volume of water that flows in t minutes from pipe = t × 0.5π m3

Radius (r2) of circular end of cylindrical tank =10/2 = 5 m

Depth (h2) of cylindrical tank = 2 m

Let the tank be filled completely in t minutes.

Volume of water filled in tank in t minutes is equal to the volume of water flowed in t minutes from the pipe.

Volume of water that flows in t minutes from pipe = Volume of water in tank

t × 0.5π = π × r22 × h2

Or, t = 100 minutes