Cylindrical 7943

The outdoor pool has a cylindrical shape with an inner diameter of 3.6 m and a depth of 1.2 m.

a) how long will it take to fill if 2 liters of water flow per second?
b) how many crowns will it cost to fill the pool? (find out the price of 1 m³ of water. )

Correct answer:

t =  1.6965 h
p =  14.6574 Eur

Step-by-step explanation:

$$\begin{gathered} D=3.6\text{m} \\ h=1.2\text{m} \\ r=D/2=3.6/2=\frac{9}{5}=1.8\text{m} \\ {S}_1=\pi \cdot r^2=3.1416\cdot 1.8^2\doteq 10.1788{\text{m}}^2 \\ V=S_1\cdot h=10.1788\cdot 1.2\doteq 12.2145{\text{m}}^3 \\ {V}_1=V\to \text{l}=V\cdot 1000\text{l}=12.2145\cdot 1000\text{l}=12214.51224\text{l} \\ Q=2\text{l/s} \\ {t}_1=V_1/Q=12214.5122/2\doteq 6107.2561\text{s} \\ t=t_1\to \text{h}=t_1:3600\text{h}=6107.2561:3600\text{h}=1.696\text{h}=1.6965\text{h} \end{gathered}$$

$$\begin{gathered} k=1.2{\text{Eur/m}}_3 \\ p=k\cdot V=1.2\cdot 12.2145=14.6574\text{Eur} \end{gathered}$$

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