Pool

How many hl of water is in a cuboid pool (a = 25m, b = 8m) if the area of the wetted walls is 279.2 m²?

Correct answer:

V =  2400 hl

Step-by-step explanation:

$$\begin{gathered} a=25\text{ m } \\ b=8\text{ m } \\ S=279.2{\text{m}}^2 \\ {S}_1=a\cdot b=25\cdot 8=200{\text{m}}^2 \\ S=S_1+2(a+b)\cdot c \\ c={\displaystyle \frac{S-S_1}{2\cdot (a+b)}}={\displaystyle \frac{279.2-200}{2\cdot (25+8)}}={\displaystyle \frac{6}{5}}=1.2\text{ m } \\ {V}_1=a\cdot b\cdot c=25\cdot 8\cdot 1.2=240{\text{m}}^3 \\ V=V_1\to \text{ hl}=V_1\cdot 10\text{ hl}=240\cdot 10\text{ hl}=2400\text{ hl}=2400\text{ hl} \end{gathered}$$

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