Pool Volume and Painting

A block-shaped pool has a length of 50 m, width of 25 m, and depth of 3.5 m. When the pool is filled 50 cm below the edge, how many hectoliters of water is in it? If we paint the inside of the pool two coats and you pay 50 cents per 1 m², how much EUR will you pay?

Final Answer:

V =  37500 hl
x =  1775 EUR

Step-by-step explanation:

$$\begin{gathered} a=50\text{m} \\ b=25\text{m} \\ {c}_1=3.5\text{m} \\ {c}_2=50\text{cm}\to \text{m}=50:100\text{m}=0.5\text{m} \\ c=c_1-c_2=3.5-0.5=3\text{m} \\ {V}_1=a\cdot b\cdot c=50\cdot 25\cdot 3=3750{\text{m}}^3 \\ V=V_1\to \text{hl}=V_1\cdot 10\text{hl}=3750\cdot 10\text{hl}=37500\text{hl}=37500\text{hl} \end{gathered}$$

$$\begin{gathered} k=0.50{\text{eur/m}}^2 \\ o=2\cdot (a+b)=2\cdot (50+25)=150\text{m} \\ S=a\cdot b+o\cdot c_1=50\cdot 25+150\cdot 3.5=1775{\text{m}}^2 \\ x=2\cdot S\cdot k=2\cdot 1775\cdot 0.5=1775\text{EUR} \end{gathered}$$

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