Pool coating

How many tiles 20 cm × 15 cm need to coat the bottom and sidewalls of the pool with bottom dimensions 75 m × 10 m if the pool can fit up to 1402500 liters of water?

Final Answer:

n =  35597

Step-by-step explanation:

$$\begin{gathered} V=1402500\text{l}\to {\text{m}}^3=1402500:1000{\text{m}}^3=1402.5{\text{m}}^3 \\ x=75\text{m} \\ y=10\text{m} \\ a=20\text{cm} \\ b=15\text{cm} \\ V=x\cdot y\cdot h \\ {S}_0=x\cdot y=75\cdot 10=750{\text{m}}^2 \\ h=\frac{V}{S_0}=\frac{1402.5}{750}=\frac{187}{100}=1\frac{87}{100}=1.87\text{m} \\ {S}_1=a\cdot b=20\cdot 15=300{\text{cm}}^2 \\ {S}_2=S_0+2\cdot h\cdot (x+y)=750+2\cdot 1.87\cdot (75+10)=\frac{10679}{10}=1067\frac{9}{10}=1067.9{\text{m}}^2 \\ {S}_3=S_2\to {\text{cm}}^2=S_2\cdot 10000{\text{cm}}^2=1067.9\cdot 10000{\text{cm}}^2=10679000{\text{cm}}^2 \\ n=S_3/S_1=10679000/300=35597 \end{gathered}$$

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