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Question
Complete the table given below:
| S.No | Solid | Shape of Solid |
Number of faces F |
Number of Verticles V |
Number of edges E |
F + V | E + 2 |
| a. | Cuboid |  |
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| b. | Triangular Pyramid |
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| c. | Square Pyramid |
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| d. | Rectangular Pyramid |
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| e. | Pentagonal Pyramid |
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| f. | Hexagonal Pyramid |
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| g. | Triangular Prism |
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| h. | Square Prism |
 |
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| i. | Cube |  |
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| j. | Pentagonal Prism |
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| k. | Octagonal Prism |
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| l. | Heptagonal Prism |
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Solution
By using Euler’s formula for polyhedron,
| S.No | Solid | Shape of Solid |
Number of faces F |
Number of Verticles V |
Number of edges E |
F + V | E + 2 |
| a. | Cuboid | |
6 | 8 | 12 | 6 + 8 = 14 | 12 + 2 = 14 |
| b. | Triangular Pyramid |
|
4 | 4 | 6 | 4 + 4 = 8 | 6 + 2 = 8 |
| c. | Square Pyramid |
|
5 | 5 | 8 | 5 + 5 = 10 | 8 + 2 = 10 |
| d. | Rectangular Pyramid |
|
5 | 5 | 8 | 5 + 5 = 10 | 8 + 2 = 10 |
| e. | Pentagonal Pyramid |
|
6 | 6 | 10 | 6 + 6 = 12 | 10 + 2 = 12 |
| f. | Hexagonal Pyramid |
|
7 | 7 | 12 | 7 + 7 = 14 | 12 + 2 = 14 |
| g. | Triangular Prism |
|
5 | 6 | 9 | 5 + 6 = 11 | 9 + 2 = 11 |
| h. | Square Prism |
|
6 | 8 | 12 | 6 + 8 = 14 | 12 + 2 = 14 |
| i. | Cube | |
6 | 8 | 12 | 6 + 8 = 14 | 12 + 2 = 14 |
| j. | Pentagonal Prism |
|
7 | 10 | 15 | 7 + 10 = 17 | 15 + 2 = 17 |
| k. | Octagonal Prism |
|
10 | 16 | 24 | 10 + 16 = 26 | 24 + 2 = 26 |
| l. | Heptagonal Prism |
|
9 | 14 | 21 | 9 + 14 = 23 | 21 + 2 = 23 |
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