Octagonal pyramid

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

Correct answer:

V =  314269.6805

Step-by-step explanation:

v=100 α=60 ∘ α1​=α=60°=1.0472=π/3 n=8  tan α = v/r  r=v/tan(α1​)=100/tan1.0472≐57.735  β=2⋅ n2π​=2⋅ 82⋅ 3.1416​≐0.3927 rad  sin β  = x / r  x=r⋅ sinβ=57.735⋅ sin0.3927≐22.0942  r2 = x2 + w2 w=r2−x2​=57.7352−22.09422​≐53.3402  S1​=2w⋅ x​=253.3402⋅ 22.0942​≐589.2557  S=2⋅ n⋅ S1​=2⋅ 8⋅ 589.2557≐9428.0904  V=31​⋅ S⋅ v=31​⋅ 9428.0904⋅ 100=314269.6805≐3.143⋅105

Try calculation via our triangle calculator.


Try another example


Did you find an error or inaccuracy? Feel free to write us. Thank you!







Tips for related online calculators
See also our right triangle calculator.
Tip: Our volume units converter will help you convert volume units.
See also our trigonometric triangle calculator.

You need to know the following knowledge to solve this word math problem:

algebrasolid geometryplanimetricsgoniometry and trigonometryUnits of physical quantitiesGrade of the word problem

 
We encourage you to watch this tutorial video on this math problem: video1

Related math problems and questions: