Hectoliters

How deep is the pool if there are 2025 hectoliters of water and the bottom dimensions are a = 15 meters b = 7,5 meters and the water level is up to 9/10 (nine-tenths) of height.

Correct result:

h =  2 m

Solution:

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

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