Advertisements
Advertisements
Question
Using Euler’s formula, find the values of a, b, c and d.
| Faces | a | 5 | 20 | 6 |
| Vertices | 6 | b | 12 | d |
| Edges | 12 | 9 | c | 12 |
Advertisements
Solution
| Faces | a | 5 | 20 | 6 |
| Vertices | 6 | b | 12 | d |
| Edges | 12 | 9 | c | 12 |
(i) a + 6 – 12 = 2
⇒ a = 2 – 6 + 12
= 14 – 6
= 8
(ii) b + 5 – 9 = 2
⇒ 6 = 2 + 9 – 5
= 6
(iii) 20 + 12 – c = 2
⇒32 – c = 2
⇒ c = 32 – 2
⇒ c = 30
(iv) 6 + d – 12 = 2
⇒ d – 6 = 2
⇒ d = 2 + 6
= 8
RELATED QUESTIONS
The given Figure are prisms or not?
Can a polyhedron have for its face 4 triangles?
Can a polyhedron have for its face a square and four triangles?
Is it possible to have a polyhedron with any given number of faces?
Verify Euler's formula for the following polyhedron:
Which among the following are nets for a cube?
Draw net for the following polyhedron :
Match the following figure:
Identify if the following net can be used to form a cube:
The following figure, given below, shows shadows of some 3D object when seen under the lamp of an overhead projector:
Verify Euler’s formula for the table given below.
| Faces | Vertices | Edges |
| 32 | 60 | 90 |
How many vertices does the following solid have?
Cone
How many vertices does the following solid have?
Sphere
How many vertices does the following solid have?
Hexagonal Prism
How many edges does the following solid have?
Sphere
Total number of edges a cylinder has ______.
The common portion of two adjacent faces of a cuboid is called ______.
A triangular prism has 5 faces, 9 edges and 6 vertices.
The corner points where edges of a solid meet are called:
What defines the edges of a solid shape?
