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  tan⁡α=v/r  r=v/tan⁡(α1)=100/tan⁡1.0472≐57.735  β=2π2⋅ n=2⋅ 3.14162⋅ 8≐0.3927 rad  sin⁡β=x/r  x=r⋅ sin⁡(β)=57.735⋅ sin⁡0.3927≐22.0942  r2=x2+w2 w=r2−x2=57.7352−22.09422≐53.3402  S1=w⋅ x2=53.3402⋅ 22.09422≐589.2557  S=2⋅ n⋅ S1=2⋅ 8⋅ 589.2557≐9428.0904  V=13⋅ S⋅ v=13⋅ 9428.0904⋅ 100=314269.6805

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