Advertisements
Advertisements
Question
Using Euler's formula find the unknown:
| Faces | ? | 5 | 20 |
| Vertices | 6 | ? | 12 |
| Edges | 12 | 9 | ? |
Advertisements
Solution
\[\text { We know that the Euler's formula is: F+V = E+2 }\]
1 .\[\text { The number of vertices V is 6 and the number of edges E is 12 }.\]
\[\text { Using Euler's formula: }\]
\[\text { F+6 = 12+2 }\]
\[\text { F+6 = 14 }\]
\[\text { F = 14-6 }\]
\[\text { F = 8 }\]
\[\text { So, the number of faces in this polyhedron is 8 }.\]
2. \[\text { Faces, F = 5 }\]
\[\text { Edges, E = 9}.\]
\[\text { We have to find the number of vertices }.\]
\[\text { Putting these values in Euler's formula: }\]
\[\text { 5+V = 9+2 }\]
\[\text { 5+V = 11 }\]
\[\text { V = 11-5 }\]
\[\text { V = 6 }\]
\[\text { So, the number of vertices in this polyhedron is 6 }.\]
3. \[\text { Number of faces F = 20 }\]
\[\text { Number of vertices V = 12 }\]
\[\text { Using Euler's formula: }\]
\[\text { 20+12 = E+2 }\]
\[\text { 32 = E+2 }\]
\[\text { E+2 = 32 }\]
\[\text { E = 32-2 }\]
\[\text { E = 30 }.\]
\[\text { So, the number of edges in this polyhedron is 30 }.\]
RELATED QUESTIONS
How are pyramids and cones alike?
Using Euler’s formula, find the unknown.
| Faces | ? | 5 | 20 |
| Vertices | 6 | ? | 12 |
| Edges | 12 | 9 | ? |
Can a polyhedron have for its face 4 triangles?
Match the following figure:
Dice are cubes with dots or dots on the face. Opposite faces of a die always have a total of seven on them.
In the given below net to make dice (cube), the numbers inserted in the square indicate the number of dots in it.
Insert suitable numbers in the blank so that numbers in opposite faces of the die have a total of seven dots.
Dice are cubes with dots or dots on the face. Opposite faces of a die always have a total of seven on them.
In the given below net to make dice (cube), the numbers inserted in the square indicate the number of dots in it.
Insert suitable numbers in the blank so that numbers in opposite faces of the die have a total of seven dots.
Verify Euler’s formula for the table given below.
| Faces | Verticles | Edges |
| 10 | 6 | 12 |
How many edges does the following solid have?
Kaleidoscope
The corners of solid shapes are called its ______.
What defines the edges of a solid shape?
