Dissecting a triangular prism into 3 equal-volume pyramids
- David Chandler
Use the slider or button to dissect the prism into three pyramids. When the separation is complete, three more buttons and sliders will appear. Use them to compare the volumes of the three pyramids. Although the pyramids are not congruent, upon pair-wise comparison it can be seen that they have the same volume, each 1/3 the volume of the original prism.
Vary the prism using the red control points, then dissect it, then compare the resulting pyramids. Note that the pyramid labeled C has the same base and altitude as the original prism. This activity demonstrates the fact that the volume of a pyramid is 1/3 of the corresponding prism with the same base and altitude.