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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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If a solid shape has 12 faces and 20 vertices, then the number of edges in this solid is ______.
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.
Look at the shapes given below and state which of these are polyhedra using Euler’s formula.
Look at the shapes given below and state which of these are polyhedra using Euler’s formula.
Look at the shapes given below and state which of these are polyhedra using Euler’s formula.
Look at the shapes given below and state which of these are polyhedra using Euler’s formula.
Using Euler’s formula, find the value of unknown x in the following table.
| 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 |
Check whether a polyhedron can have V = 12, E = 6 and F = 8.
