Cracked aquarium

Martin wanted to glue together an aquarium with his father's help. In the manual he read that it should have a volume of 45 litres. On the table he did not have much space. The bottom of the aquarium could have dimensions of only 25 cm and 40 cm. How tall must the aquarium be so that the required amount of water fits in it? How many dm square of glass will Martin need if he wants to have the aquarium covered also at the top? Please calculate with the understanding of a 6th grade pupil. Thank you very much

Final Answer:

c =  45 cm
S =  78.5 dm²

Step-by-step explanation:

$$\begin{gathered} a=25\text{cm} \\ b=40\text{cm} \\ V=45\text{l}\to {\text{cm}}^3=45\cdot 1000{\text{cm}}^3=45000{\text{cm}}^3 \\ V=abc \\ c=V/(a\cdot b)=45000/(25\cdot 40)=45\text{cm} \end{gathered}$$

$$\begin{gathered} S_1=2\cdot (a\cdot b+b\cdot c+a\cdot c)=2\cdot (25\cdot 40+40\cdot 45+25\cdot 45)=7850{\text{cm}}^2 \\ S=S_1\to {\text{dm}}^2=S_1:100{\text{dm}}^2=7850:100{\text{dm}}^2=78.5{\text{dm}}^2=78.5{\text{dm}}^2 \end{gathered}$$

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