Dimensions 67534

Peter has an aquarium at home in the shape of a cuboid with 6 x 3 dm bottom dimensions and a height of 4 dm. They filled the aquarium with water according to the seller's order, 5 cm below the edge.
A) The maximum number of fish can be raised in it if 1 fish needs 6 liters of water.
B) After a week, the water level decreased by 1 cm. How many liters of water are left in the aquarium?

Correct answer:

n =  10
V₃ =  61.2 l

Step-by-step explanation:

$$\begin{gathered} a=6\text{dm} \\ b=3\text{dm} \\ c=4-0.5=3.5\text{dm} \\ V=a\cdot b\cdot c=6\cdot 3\cdot 3.5=63{\text{dm}}^3 \\ {V}_1=6\text{l}\to {\text{dm}}^3=6\cdot 1{\text{dm}}^3=6{\text{dm}}^3 \\ n=\lfloor V/V_1\rfloor =\lfloor 63/6\rfloor =10 \end{gathered}$$

$$\begin{gathered} d=1\text{cm}\to \text{dm}=1:10\text{dm}=0.1\text{dm} \\ {V}_4=a\cdot b\cdot d=6\cdot 3\cdot 0.1=\frac{9}{5}=1.8{\text{dm}}^3 \\ {V}_3=V-V_4=63-1.8=61.2\text{l} \end{gathered}$$

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