Respuesta :
Answer:
Approximately 4.58 minutes.
Step-by-step explanation:
The diameter of hose is in centimeters, that is 2.9 cm.
Velocity is in m/s that can be converted into cm/s.
Let the velocity be 'v'.
v = 3.3 m/s= 330 cm/s
The amount of water following through the cross sectional area of the hose is.
[tex]A = \pi \times r^2[/tex]
diameter = 2.9 cm
[tex]r = 1.45 cm[/tex]
[tex]A =\pi \times (1.45)^2[/tex]
[tex]A = 3.14 \times 2.10[/tex]
[tex]A = 6.601 cm^2[/tex]
The cross sectional are of the hose is approximately [tex]6.60 cm^2[/tex]. To volume of water that flows through the hose each second, multiply its velocity by the cross sectional area of the hose.
Volume/ second = [tex]330 \times 6.60 =2178.61 cm^3/s[/tex]
This is approximately [tex]2718.61 cm^3/s[/tex]. There are [tex]1000 cm^3[/tex] in one liter.
Total volume [tex]= 600 \times 1000 = 600,000 cm^3[/tex]
To determine the time in seconds, divide the total volume by the volume per second.
t = [tex]\frac{600,000}{2178.61} = 275.40 s[/tex]
This is roughly 275 seconds.
We can convert 275 seconds into minutes.
t (mins) = [tex]{275 \over 60 }=4.58[/tex] minutes.
So it will take 4.58 minutes to fill the wading pool.
