Hectoliters

How deep is the pool if there are 2025 hectoliters of water, the bottom dimensions are a = 15 meters b = 7.5 meters, and the water level is up to 9/10 (nine-tenths) of the height?

Correct answer:

h =  2 m

Step-by-step explanation:

$$\begin{gathered} V=2025\text{hl}\to {\text{m}}^3=2025:10{\text{m}}^3=202.5{\text{m}}^3 \\ a=15\text{m} \\ b=7.5\text{m} \\ S=a\cdot b=15\cdot 7.5=\frac{225}{2}=112.5{\text{m}}^2 \\ c=V/S=\frac{405}{2}/\frac{225}{2}=\frac{405}{2}:\frac{225}{2}=\frac{405}{2}\cdot \frac{2}{225}=\frac{405\cdot 2}{2\cdot 225}=\frac{810}{450}=\frac{9}{5}=1.8\text{m} \\ c=\frac{9}{10}h \\ h=\frac{10}{9}\cdot c=\frac{10}{9}\cdot \frac{9}{5}=\frac{10\cdot 9}{9\cdot 5}=\frac{90}{45}=2\text{m} \end{gathered}$$

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