# Volume of Pyramids (method 1)

## Prove that volume of a pyramid is 1/3 the volume of cube

A pyramid is a polyhedron with one base that is any polygon . Its other faces are triangles. The volume of a 3 -dimensional solid is the amount of space it occupies. Volume is measured in cubic units ( in^3,ft^3,cm^3,m^3 , etc). Be sure that all of the measurements are in the same unit before computing the volume. The volume V of a pyramid is one-third the area of the base B times the height h. V=1/3 * B* h where B is the area of the base and h is the height of the pyramid.Proof of the Formula Proof In the given figure below ﻿ ﻿ Volume of Cube = Volume of 3 pyramids or Volume of Pyramid= x Volume of Cube (Cube र Pyramid को base area र उचाई एउटै छ )

## Construct Pyramids under a given Cube to prove that volume of a pyramid is 1/3 the volume of cube with following portocal.

1.      Open a new GeoGebra window 2.      Switch to Perspectives → 3D Graphing 3.      Add Graphics view to the workspace 4.      Activate Graphics and create a slider rotation running from 00 to 900 with increment 10 ﻿a.       Click on slider tool ﻿b.      Select angle ﻿c.       Give name as rotation ﻿d.      Give minimum value 00, maximum value 900, and increment 10 5. Using Input Box, create three points ﻿A=(2,0,0), ﻿B=(2,2,0) ﻿and C=(0,2,0) 6. Using Input Box, construct a cube as below cube=Cube(A,B,C) 7. Using Input Box, construct a pyramid Pyr1=Pyramid(A, E, C, D, F) 8. Using Input Box, construct a pyramid Pyr2=Pyramid(A, E, C, D, F) 9. Using Input Box, construct a pyramid Pyr3=Pyramid(A, E, C, D, F) 10. Using Input Box, construct a line ﻿ ﻿ax2=Line(D,A) Hide ax2 10. Using Input Box, construct a line ﻿ ﻿ax3=Line(D,C) Hide ax3 11. Using Input Box, construct a transformation ﻿ ﻿Rot2=Rotate(Pyr2, rotation, ax2) ﻿ ﻿Hide Pyr2 11. Using Input Box, construct a transformation ﻿ ﻿Rot3=Rotate(Pyr3, rotation, ax3) ﻿ ﻿Hide Pyr3 Now, design the layouts as much as interactive with text and color features