Pool filling time

The garden children's pool has the shape of a cylinder with a base diameter of 3.2 m and a depth of 60 cm. How many hours and minutes will it fill 10 cm below the edge of 0.5 l of water per second flows through the tributary? Round to whole minutes and write in the form of h and min.

Result

t = 2:14 hh:mm

Step-by-step explanation:

$$\begin{gathered} D=3.2\text{m}\to \text{dm}=3.2\cdot 10\text{dm}=32\text{dm} \\ {h}_1=60\text{cm}\to \text{dm}=60:10\text{dm}=6\text{dm} \\ {h}_2=10\text{cm}\to \text{dm}=10:10\text{dm}=1\text{dm} \\ h=h_1-h_2=6-1=5\text{dm} \\ r=D/2=32/2=16\text{dm} \\ S=\pi \cdot r^2=3.1416\cdot 16^2\doteq 804.2477{\text{dm}}^2 \\ V=h\cdot S=5\cdot 804.2477\doteq 4021.2386\text{l} \\ Q=0.5\text{l/s} \\ {t}_1=V/Q=4021.2386/0.5\doteq 8042.4772\text{s} \\ t=t_1/3600=8042.4772/3600=\frac{81057}{36283}=2.23402=2:14\text{hh}:\text{mm} \end{gathered}$$

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