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 3 km/hr, in how much time will the tank be filled

Answer 1

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  = $\pi r^2h$

Where r is the radius of the pipe

r = $\frac{diameter}{2}$

r = $\frac{20}{2}$

r = 10cm = $\frac{1}{10}$

The volume of the pipe

=> $\pi (\frac{1}{10})^2 h$

=> $\frac{1}{100}\pi h$

=> $\frac{\pi h}{100}$-----------------------------------(1)

Step 2: Finding the volume of the tank

The volume of the tank = $\pi r^2h$

Where r is the radius of the tank

r = $\frac{diameter}{2}$

r = $\frac{10}{2}$

r = 5

The volume of the pipe

=> $(\pi )(5)^2 (2)$

=> $50 \pi$-------------------------------------(2)

Equating (1) and (2)

$\frac{\pi h}{100}$ =  $50 \pi$

$\frac{h}{100}$ =  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  = $\frac{1}{3}$ hours

To Travel 5 km

=> $5 \times \frac{1}{3}$ hours

=> $\frac{5}{3}$ hours

converting into minutes

=> $\frac{5}{3} \times 60$

=>$\frac{300}{3}$

=> 100 minutes