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Question
A polyhedron can have 10 faces, 20 edges and 15 vertices.
Options
True
False
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Solution
This statement is False.
Explanation:
We know that, Euler’s formula satisfies for every polyhedron.
i.e. F + V – E = 2
Here, F = 10, E = 20
And V = 15
On putting these values in the Euler’s formula, we get
10 + 15 – 20 = 2
⇒ 25 – 20 = 2
⇒ 5 ≠ 2
Hence, the given values does not satisfy the Euler’s formula.
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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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Look at the shapes given below and state which of these are polyhedra using Euler’s formula.
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| Faces | 7 |
| Vertices | 10 |
| Edges | x |
Using Euler’s formula, find the value of unknown r in the following table.
| Faces | 8 |
| Vertices | 11 |
| Edges | r |
A polyhedron has 60 edges and 40 vertices. Find the number of its faces.
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A solid has forty faces and sixty edges. Find the number of vertices of the solid.
