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?

Result

V =  2400 hl

Solution:

a=25 m b=8 m S=279.2 m2  S1=a⋅ b=25⋅ 8=200 m2 S=S1+2(a+b)⋅ c c=S−S12⋅ (a+b)=279.2−2002⋅ (25+8)=65=1.2 m  V1=a⋅ b⋅ c=25⋅ 8⋅ 1.2=240 m3  V=V1→hl=V1⋅ 10 hl=2400 hl=2400 hla=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=\dfrac{ S-S_{1} }{ 2 \cdot \ (a+b) }=\dfrac{ 279.2-200 }{ 2 \cdot \ (25+8) }=\dfrac{ 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} \rightarrow hl=V_{1} \cdot \ 10 \ hl=2400 \ hl=2400 \ \text{hl}

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