Question

A garden hose has a radius of 0.0120 m, and water comes out at a speed of 4.88 m/s. How much time does it take to fill up a kids swimming pool with a volume of 3.88 m^3

Answer 1

Correct Answer:

1758 seconds

Answer 2

The radius of the garden hose is $r=0.0120 m$, so its cross-sectional area is
$A=\pi r^2 = \pi (0.0120 m)^2 = 4.52 \cdot 10^{-4} m^2$

The amount of water (in $m^3$) that comes out from the hose in one second is given by the product between the speed of the water and the cross-sectional area of the hose:
$V_w = A v = (4.52 \cdot 10^{-4}m^2)(4.88 m/s)=2.2 \cdot 10^{-3} m^3/s$

The time needed to fill the pool is equal to the volume of the pool divided by the amount of water that comes out every second:
$t= \frac{V}{V_w}= \frac{3.88 m^3}{2.2 \cdot 10^{-3}m^3}=1758 s$