Octagonal pyramid

Find the volume of a regular octagonal pyramid with height v = 100 and the angle of the side edge with the plane of the base is α = 60°.

Correct result:

V =  314269.6805

Solution:

v=100 α=60 α1=α=60=1.0472=π/3 n=8  tanα=v/r  r=v/tan(α1)=100/tan1.047257.735  β=2π2 n=2 3.14162 80.3927 rad  sinβ=x/r  x=r sin(β)=57.735 sin0.392722.0942  r2=x2+w2 w=r2x2=57.735222.0942253.3402  S1=w x2=53.3402 22.09422589.2557  S=2 n S1=2 8 589.25579428.0904  V=13 S v=13 9428.0904 100=314269.6805=3.143105

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