Aquarium Dimensions and Volume

The aquarium dimensions are in the ratio a: b: c = 5:2:4. 6600 cm² of glass was used for its production. How many liters of water will fit in the aquarium if it reaches 5 cm below its edge?

Final Answer:

V =  35 l

Step-by-step explanation:

$$\begin{gathered} S=6600{\text{cm}}^2\to {\text{dm}}^2=6600:100{\text{dm}}^2=66{\text{dm}}^2 \\ a:b:c=5:2:4 \\ a=5x \\ b=2x \\ c=4x \\ S=a\cdot b+2\cdot c\cdot (a+b) \\ 5x\cdot 2x+2\cdot 4x\cdot (5x+2x)=S \\ 66x^2-66=0 \\ {x}^2-1=0 \\ {x}^2=1 \\ x=\sqrt{1}=1\text{dm} \\ a=5\cdot x=5\cdot 1=5\text{dm} \\ b=2\cdot x=2\cdot 1=2\text{dm} \\ c=4\cdot x=4\cdot 1=4\text{dm} \\ {c}_1=5\text{cm}\to \text{dm}=5:10\text{dm}=0.5\text{dm} \\ 1liter=1d{m}^3 \\ V=a\cdot b\cdot (c-c_1)=5\cdot 2\cdot (4-0.5)=35=35\text{l} \\ \text{ Verifying Solution: } \\ {S}_2=a\cdot b+2\cdot c\cdot (a+b)=5\cdot 2+2\cdot 4\cdot (5+2)=66{\text{dm}}^2 \end{gathered}$$

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