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Concept · Geometry & Algebra
3D analysis in a cube
moving points, skew-line angle ranges, perpendicularity, constant-volume pyramids, loci and path lengths
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Key formulas
9- 3D point P(x,y,z)3D distance AB = √(x2−x1)2 + (y2−y1)2 + (z2−z1)2
- Cuboid volume = lwhsurface = 2(lw+lh+wh)cube volume = s3, surface = 6s2
- CylinderV = πr2 h, S = 2πr2 + 2πrh
- ConeV = (1/3)πr2 h, lateral S = πrl, total S = πrl + πr2, slant l = √r2+h2
- SphereV = (4/3)πR3, S = 4πR2
- Cone lateral unrolls to a sectorarc length 2πr = l·(central angle)base radius r = l·(angle)/(2π)
- Tetrahedron from coordinatesV = (1/6)|scalar triple product|pyramid V = (1/3)·base·height
- Oblique (cavalier) projection area ratioS' = (√2/4) S
- Equilateral triangle of side sarea = (√3/4)s2
Shaky underneath?
If the concept underneath still feels loose, patch it here before coming back to CSCA questions.
FoundationsPrecalculus bridgeAlgebra 2 foundations