Aquarium 20

Martin wanted to help his father build an aquarium. He read in the manual that it should have a volume of 45 litres. However, he did not have much space on the table; the base of the aquarium could be at most 25 cm by 40 cm. How tall does the aquarium need to be to hold the required amount of water? How many dm² of glass will Martin need if he wants to have the aquarium covered at the top as well?

Final Answer:

c =  45 cm
S =  78.5 dm²

Step-by-step explanation:

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

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

Try another example