Volume of Pyramids (method 1)
- Bed Prasad Dhakal
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