a farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank in his field - Maths - Surface Areas and Volumes

Question

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

Vimala · Accepted Answer

Let x hours be the time taken for the pipe to fill the tank.

Since the water is flowing at the rate of 3 Km/h, Therefore,

Length of the water column in x hours is $3 x K m = 3000 x m$

Therefore, the length of the pipe is $3000 x m$

The radius of the pipe is

$\frac{20}{2} c m = 10 c m = \frac{10}{100} m = 0.1 m$

Therefore, the volume of the water flowing through the pipe in x hours is

$V_{1} = π \times {0.1}^{2} \times 3000 x m^{3} .......... (1)$

Also, Volume of the water that falls into the tank in x hours is

$V_{2} = π \times 5^{2} \times 2 m^{3} .......... (2)$

We have the volume of the water flowing through the pipe in x hours = Volume of the water that falls into the tank in x hours

Thus equate equations (1) and (2)

$π \times 0.1 \times 0.1 \times 3000 x = π \times 5 \times 5 \times 2 \Rightarrow 30 x = 50 x \Rightarrow x = \frac{50}{30} h o u r \Rightarrow x = \frac{5}{3} \times 60 \min u t e s \Rightarrow x = 100 \min u t e s$

Thus, the water in the tank will fill in 100 minutes.

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