Garden pool

Mr. Novak fills the garden pool (cylinder; diameter of 200 cm) with 31.4 hl of water. What is the depth of the pool when the water level is 10 cm below the upper edge of the pool?

Final Answer:

h =  109.95 cm

Step-by-step explanation:

$$\begin{gathered} D=200\text{cm} \\ V=31.4\text{hl}\to {\text{dm}}^3=31.4\cdot 100{\text{dm}}^3=3140{\text{dm}}^3 \\ {V}_2=V\to {\text{cm}}^3=V\cdot 1000{\text{cm}}^3=3140\cdot 1000{\text{cm}}^3=3140000{\text{cm}}^3 \\ {h}_2=10\text{cm} \\ r=D/2=200/2=100\text{cm} \\ V=\pi r^2{h}_1 \\ {h}_1=\frac{V_2}{\pi \cdot r^2}=\frac{3140000}{3.1416\cdot 100^2}\doteq 99.9493\text{cm} \\ h=h_1+h_2=99.9493+10=109.95\text{cm} \end{gathered}$$

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