Dimensions of an aquarium

The large aquarium is shaped like a cuboid and has dimensions in the ratio 5: 7: 4. The sum of the lengths of all edges is 96 dm. How many liters of water will be in the aquarium if it is filled to four-fifths?

Correct answer:

V =  24192 l

Step-by-step explanation:

$$\begin{gathered} a:b:c=5:7:4 \\ a+b+c=96\text{dm} \\ a=\frac{5}{5+7+4}\cdot 96=30\text{dm} \\ b=\frac{7}{5+7+4}\cdot 96=42\text{dm} \\ c=\frac{4}{5+7+4}\cdot 96=24\text{dm} \\ 1l=1d{m}^3 \\ {V}_1=a\cdot b\cdot c=30\cdot 42\cdot 24=30240\text{l} \\ V=\frac{4}{5}\cdot V_1=\frac{4}{5}\cdot 30240=\frac{4\cdot 30240}{5}=\frac{120960}{5}=24192\text{l} \end{gathered}$$

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