Octagonal tank

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

Correct result:

S =  187.456 m2

Solution:

a=3 m b=6 m  S1=8 a b=8 3 6=144 m2 S2=2 (1+2) a2=2 (1+2) 3243.4558 m2  S=S1+S2=144+43.4558=187.456 m2a=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=187.456 \ \text{m}^2



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