Half Full Height with Geo Gebra Geo Gebra

Half Full Height with Geo. Gebra

Geo. Gebra Model Printable Nets (Cut & Fold)

§ The volume of a right rectangular prism (a box) Dice Template (Cut & Fold) is LWH = height × (area of the base). Bricks Template (Cut & Fold) § By Cavalieri’s Principle, the volume of any prism is height × (area of the base). § A cylinder can also be verified by calculus. Geo. Gebra Model of Cavalieri

§ Geometric Argument by decomposition § Any pyramid (including cone) by Cavalieri’s Principle Geo. Gebra Model Printable Nets (Cut & Fold) More General Case (GGB) Printable Nets

§ Square Pyramid by Integration A similar argument can be used for a cone to get V= (1/3)πr 2 h.

§ By decomposition, Volume of tetrahedron = 1/6 × (Volume of Parallelepiped) Geo. Gebra Construction Printable Cut & Fold Net (with case)

§ When opposite side are “perpendicular”, Volume = 1/6 × h × product of these side lengths.

§ Volume by Algebra

§ Volume of frustum of cone by calculus

§ Pyramids by Decomposition(s) b Geo. Gebra Model Printable Nets (Cut & Fold)

Tom Banchoff’s Dissection Geo. Gebra Model Printable Nets (Cut & Fold)

Geo. Gebra Model Four Piece Dissection Printable Nets (Cut & Fold)

§ Volume by decomposition(s) Geo. Gebra Model Printable Nets (Cut & Fold)

Printable Nets (Cut & Fold) Aha!!! Eureka! “Wallah”

§ Archimedes’ Argument https: //www. geogebra. org/m/wecxcyhx

https: //www. mathalino. com/r eviewer/derivationformulas/derivation-formulavolume-sphere-integration