Octagonal tank

The tank has the shape of a regular octagonal prism without an upper base. The base edge has a = 3m, and the side edge b = 6m. How much metal sheet is needed to build the tank? Do not think about losses or sheet thickness.

Correct answer:

S =  187.4558 m²

Step-by-step explanation:

$$\begin{gathered} a=3\text{m} \\ b=6\text{m} \\ {S}_1=8\cdot a\cdot b=8\cdot 3\cdot 6=144{\text{m}}^2 \\ {S}_2=2\cdot (1+\sqrt{2})\cdot a^2=2\cdot (1+\sqrt{2})\cdot 3^2\doteq 43.4558{\text{m}}^2 \\ S=S_1+S_2=144+43.4558=187.4558{\text{m}}^2 \end{gathered}$$

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