Dimensions - pool

The swimming pool dimensions are as follows: l:w:h = 10:4:1. The pool can hold 625 m³ of water. Calculate how many square meters of tiles need to be purchased for lining the pool walls if we add 5% for waste.

Final Answer:

S =  446.25 m²

Step-by-step explanation:

$$\begin{gathered} V=625{\text{m}}^3 \\ a:b:c=10:4:1=10x:4x:1x \\ V=abc \\ V=10x\cdot 4x\cdot x=40\cdot x^3 \\ x=\sqrt[3]{V/40}=\sqrt[3]{625/40}=\frac{5}{2}=2.5\text{m} \\ a=10\cdot x=10\cdot 2.5=25\text{m} \\ b=4\cdot x=4\cdot 2.5=10\text{m} \\ c=x=2.5=\frac{5}{2}=2.5\text{m} \\ o=2\cdot (a+b)=2\cdot (25+10)=70\text{m} \\ {S}_1=a\cdot b+o\cdot c=25\cdot 10+70\cdot 2.5=425\text{m} \\ q=100\%+5\%=1+\frac{5}{100}=1.05 \\ S=q\cdot S_1=1.05\cdot 425=446.25{\text{m}}^2 \end{gathered}$$

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