If a Polyhedron Has 10 Faces and 8 Vertices, Find the Number of Edges in It. - Mathematics

Advertisements
Advertisements
Sum

If a polyhedron has 10 faces and 8 vertices, find the number of edges in it.

Advertisements

Solution

Faces = 10
Vertices = 8
using Eulers formula,
F + V – E = 2
10 + 8 – E = 2
-E = 2 – 18
E= 16

  Is there an error in this question or solution?
Chapter 19: Representing 3-D in 2-D - Exercise 19 [Page 220]

APPEARS IN

Selina Concise Mathematics Class 8 ICSE
Chapter 19 Representing 3-D in 2-D
Exercise 19 | Q 1 | Page 220

RELATED QUESTIONS

Can a polyhedron have for its faces 3 triangles?


How are prisms and cylinders alike?


Can a polyhedron have 10 faces, 20 edges and 15 vertices?


Here is an incomplete net for making a cube. Complete it in at least two different ways. Remember that a cube has six faces. How many are there in the net here? (Give two separate diagrams. If you like, you may use a squared sheet for easy manipulation.)


Name the polyhedron that can be made by folding net:


Name the polyhedron that can be made by folding net:


If a polyhedron has 10 vertices and 7 faces, find the number of edges in it.


State, the number of faces, number of vertices and number of edges of:
(i) a pentagonal pyramid
(ii) a hexagonal prism


Dice are cubes where the sum of the numbers on the opposite faces is 7. Find the missing numbers a, b and c.


Draw at least three different nets for making a cube.


The figure, given below, shows shadows of some 3D object when seen under the lamp of an overhead projector:


   A square

In this case, name the object.


The figure, given below, shows shadows of some 3D object when seen under the lamp of an overhead projector:


     A rectangle

In this case, name the object.


The figure, given below, shows shadows of some 3D object when seen under the lamp of an overhead projector:


   A triangle

In this case, name the object.


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

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.


The following figure represent the nets of some solid. Name the solid


The following figure represent the nets of some solid. Name the solid


Identify if the following net can be used to form a cube:


The dimensions of a cuboid are 6 cm, 4 cm and 3 cm. Draw two different types of oblique sketches for this cuboid.


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 Verticles Edges
4 4 6

Verify Euler’s formula for the table given below.

Faces Verticles Edges
10 6 12

Verify Euler’s formula for the table given below.

Faces Verticles Edges
12 20 30

Verify Euler’s formula for the table given below.

Faces Vertices Edges
20 13 30

Verify Euler’s formula for the table given below.

Faces Vertices Edges
32 60 90

Using Euler’s formula, find the unknowns.

Faces Vertices Edges
? 6 14

Using Euler’s formula, find the unknowns.

Faces Vertices Edges
8 ? 10

Using Euler’s formula, find the unknowns.

Faces Verticles Edges
20 10 ?

How many vertices does the following solids have?

Sphere


How many vertices does the following solids have?

Octagonal Pyramid


How many vertices does the following solids have?

Hexagonal Prism


All faces of a pyramid are always ______.


A solid that has only one vertex is ______.


Total number of edges a cylinder has ______.


The common portion of two adjacent faces of a cuboid is called ______.


A plane surface of a solid enclosed by edges is called ______.


The corners of solid shapes are called its ______.


A cylinder has no vertex.


A triangular prism has 5 faces, 9 edges and 6 vertices.


How many faces does figure have?


Find the number of faces in the given shapes:


Find the number of faces in the given shapes:


Share
Notifications



      Forgot password?
Use app×