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geometry-All-the-edges-of-a-regular-square-pyramid-have-a-length-of-8-What-is-the-volume-




Question Number 134713 by bramlexs22 last updated on 06/Mar/21
geometry  All the edges of a regular square pyramid have a length of 8. What is the volume?
geometryAll the edges of a regular square pyramid have a length of 8. What is the volume?
Answered by john_santu last updated on 06/Mar/21
Reguler square pyramid already  a regular quadrilateral.  An equilateral triangle is two of  mirrored acroos the long leg  30°−60°−90° right the triangles  with sides in the ratio 1 : (√3) : 2 ,   The altitude of face triangle is  ((√3)/2) × 8 = 4(√3) . That triangle is   tilted in so the top vertex is over   the center of square 4 units from the  edge : h^2  + 4^2  = (4(√3))^2 ⇒h=4(√2)  so the Volume = (1/3)A.h = (1/3)×8^2  × 4(√2)  Vol = ((256(√2) )/3) units^3  •
Regulersquarepyramidalreadyaregularquadrilateral.Anequilateraltriangleistwoofmirroredacroosthelongleg30°60°90°rightthetriangleswithsidesintheratio1:3:2,Thealtitudeoffacetriangleis32×8=43.Thattriangleistiltedinsothetopvertexisoverthecenterofsquare4unitsfromtheedge:h2+42=(43)2h=42sotheVolume=13A.h=13×82×42Vol=25623units3

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