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 m³? ? s

Explanation:

Step1: Calculate the cross - sectional area of the hose

The cross - sectional area \(A\) of a circular hose is given by the formula \(A=\pi r^{2}\), where \(r = 0.0120\space m\).
\(A=\pi\times(0.0120)^{2}=\pi\times0.000144\approx 4.5239\times 10^{- 4}\space m^{2}\)

Step2: Calculate the volume flow rate \(Q\)

The volume flow rate \(Q\) is given by the product of the cross - sectional area \(A\) and the speed \(v\) of the fluid. So \(Q = A\times v\), where \(v = 4.88\space m/s\).
\(Q=4.5239\times 10^{-4}\space m^{2}\times4.88\space m/s\approx2.2077\times 10^{-3}\space m^{3}/s\)

Step3: Calculate the time \(t\) to fill the pool

The time \(t\) is given by the formula \(t=\frac{V}{Q}\), where \(V = 3.88\space m^{3}\) is the volume of the pool.
\(t=\frac{3.88}{2.2077\times 10^{-3}}\approx1757.5\space s\)

Answer:

\(1758\space s\) (rounded to a reasonable number of significant figures)