Calculate 64644

The aquarium has a length of 5dm and a width of 4dm and contains 60 liters of water.
A) calculate the height of the aquarium if the water reaches 5 cm below the edge
B) calculate the total volume of the aquarium

Correct answer:

c =  35 cm
V =  70 l

Step-by-step explanation:

$$\begin{gathered} a=5\text{dm}\to \text{cm}=5\cdot 10\text{cm}=50\text{cm} \\ b=4\text{dm}\to \text{cm}=4\cdot 10\text{cm}=40\text{cm} \\ V=60\text{l}\to {\text{cm}}^3=60\cdot 1000{\text{cm}}^3=60000{\text{cm}}^3 \\ d=5\text{cm} \\ V=a\cdot b\cdot (c-d) \\ c=d+\frac{V}{a\cdot b}=5+\frac{60000}{50\cdot 40}=35\text{cm} \end{gathered}$$

$$\begin{gathered} V_1=a\cdot b\cdot c=50\cdot 40\cdot 35=70000{\text{cm}}^3 \\ V=V_1\to \text{l}=V_1:1000\text{l}=70000:1000\text{l}=70\text{l}=70\text{l} \end{gathered}$$

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