Aquarium 20

Martin wanted to help his father glue together an aquarium. He read in the manual that it should have a volume of 45 liters. But he didn't have much space on the table, the bottom of the aquarium could only be 25 cm and 40 cm. How high does the aquarium have 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?

Correct 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