B2 In the trade, there are three aquariums in the shape of cubes, all with the same volume. Some of the internal dimensions of the aquariums are shown in the table.

|  | length | width | height |
| :---: | :---: | :---: | :---: |
| 1st aquarium | $4 d m$ | $6 d m$ | $0.5 \mathrm{~m}$ |
| 2nd aquarium | $2 d m$ | $10 d m$ |  |
| 3rd aquarium |  |  |  |

A What is the maximum number of liters of water that can be poured into each aquarium?

B What is the internal height of the 2nd aquarium?

C The 3rd aquarium has the shape of a cube. Determine the external length of the base of the aquarium to the nearest millimeter, if the glass is $6 \mathrm{~mm}$ thick!

D In the first aquarium, $75 \%$ of the volume is filled with water. To what height does the water reach in the aquarium?

E In how many different ways can the three aquariums be arranged in a row on a shelf, if the aquarium in the shape of a cube must be at the first or last position from the left or right?

F If an empty aquarium is filled with five identical sources, it fills in 1.2 minutes. In what time will an empty aquarium be filled if it is filled with only two sources?
B2 Each aquarium holds $V=4 \mathrm{dm} \cdot 6 \mathrm{dm} \cdot 5 \mathrm{dm}=120 \mathrm{l}$. The volume of the second aquarium is $120 \mathrm{dm}^{3}$. From the equation $120 \mathrm{dm}^{3}=2 \mathrm{dm} \cdot 10 \mathrm{dm} \cdot v$ we calculate the height $v=6 \mathrm{dm}$.

From the equation for the volume of a cube $120 \mathrm{dm}^{3}=a^{3}$ we calculate the inner edge $a=4.93 \mathrm{dm}$. Considering the thickness of the glass $6 \mathrm{~mm}$, the outer edge of the aquarium is $4.93 \mathrm{dm}+2 \cdot 0.06 \mathrm{dm}=5.05 \mathrm{dm}$. $75 \%$ of the water from $120 l=90 l$. From the equation for the volume of the aquarium $90 l=4 \mathrm{dm} \cdot 6 \mathrm{dm} \cdot v$ we calculate the height of the aquarium $v=3.75 \mathrm{dm}$.

If the cubic aquarium is on the first place from the left, the other two can be arranged in 2 ways. If the cubic aquarium is on the first place from the right, this means two more different ways. In total, they can be arranged in 4 different ways.

If we fill the aquarium with one source, it takes $1.2 \mathrm{~min} \cdot 5=6 \mathrm{~min}$. When filling it with two sources, the time is half as long, which is 3 min.

A Finding: The volume of each aquarium is 120 l....................................... 1 p

![](https://cdn.mathpix.com/cropped/2024_06_07_7bf2b29f7493f2ef25deg-6.jpg?height=60&width=1648&top_left_y=2083&top_left_x=267)

C The length of the outer edge is $5.05 \mathrm{dm}$. ....................................................... 2 p

![](https://cdn.mathpix.com/cropped/2024_06_07_7bf2b29f7493f2ef25deg-6.jpg?height=63&width=1662&top_left_y=2216&top_left_x=254)

E We can arrange them in a maximum of 4 ways. ................................................. 1 p

![](https://cdn.mathpix.com/cropped/2024_06_07_7bf2b29f7493f2ef25deg-6.jpg?height=63&width=1648&top_left_y=2353&top_left_x=267)