The Euler\'s formula states that F + V -E = 2 where F, V, and E represents the N

Question

The Euler's formula states that F + V -E = 2 where F, V, and E represents the Numbers of faces, vertices, and edges respectively. Verify that the formula holds for each of the following 3D solids by filling in the entries in the table. 1. The Euler's Formula states that F 2 where F, and Erepresents the number of faces. by vertices, and edges respectively. Verify that the formula holds for each of the following 3D solids filling in the entries in the table. F V- E 5 6 Triangular prism 8 Rectangular prism gon Prism 6-gon prism 21 gon prism gon prism

Explanation / Answer

Please find the table below: All the missing values have been marked in bold.

F V E F+V-E Triangular Prism 5 6 9 5+6-9=2 Rectangular Prism 6 8 12 6+8-12=2 5-gon Prism 7 10 15 7+10-15=2 6-gon Prism 8 12 18 8+12-18=2 7-gon Prism 9 14 21 9+14-21=2 n-gon Prism n+2 2n 3n n+2+2n-3n=2

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