Euler's Formula

Q.

How many edges are there in a cube?

Q. Using Euler's formula find the number of faces of polyhedron having 6 vertices and 12 edges.

Q.

Verify Euler’s relation for each of the following: (i) A square prism (ii) A tetrahedron (iii) A triangular prism (iv) A square pyramid

Q. In a solid if F = V = 5, then find the number of edges of the solid.

1. 6
2. 7
3. 5
4. 8

Q.

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

Q. How many edges does a polyhedron have which has four faces and four vertices?

Q.

Can a polyhedron have 20 faces, 12 vertices and 30 edges?

1. Rectangular prism

2. Triangular prism

Q.

What is the number of faces in a polyhedron with 10 edges and 6 vertices?

1. 8

2. 4

3. 5

4. 6

Q.

Verify Eulers formulae $V+F-E=2$ in case of : Cone

Q. Verify Euler, s relation for pyramid whose base is a polygon of n-side.

Q. Question 62

Complete the table given below:

Q. Question 17

Which of the following cannot be true for a polyhedron?
(a) V = 4, F = 4, E = 6
(a) V = 6, F = 8, E = 12
(a) V = 20, F = 12, E = 30
(a) V = 4, F = 6, E = 6

Q.

How many edges are there in a square pyramid?

Q.

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

Q.

Verify Euler's formula for the following three dimentional figures:

Q.

What is the number of edges in a pyramid with pentagon as base?

1. 10

2. 6

3. 8

4. 12

Q.

Can a polyhedron have 7 faces, 10 vertices and 15 edges?

1. Cuboid

2. Cone

Q.

Verify Eulers formulae $V+F-E=2$ in case of : sphere

Q. A polyhedron has 11 faces and 18 vertices. Find the number of edges.

1. 27
2. 33
3. 21
4. 15

Q.

A tetrahedron has $4$ faces and $6$ edges. How many vertices does it have?

Q. Question 76

A solid has forty faces and sixty edges. Find the number of vertices of the solid.

Q.

A polyhedron can have 10 faces, 6 vertices and 14 edges.

1. True

2. False

Q.

Verify Euler’s formula for these solids.

(i)	(ii)

Q.

A polyhedron with 26 edges, and 16 vertices have ___ faces.

1. 16

2. 14

3. 10

4. 12

Q.

Can a polyhedron have 14 faces, 34 edges and 33 vertices?

1. Yes

2. No

Q. What is the minimum number of faces required for a polyhedron?

1. 2
2. 3
3. 4
4. 5

Q.

What is the number of vertices in prism with triangular base?

1. 6

2. 8

3. 5

4. 10

Q. Question 6 (ii)
Verify Euler’s formula for these solids.

Q. Question 70 (iv)

Using Euler's formula. Find the value of unknown.

Faces p
vertices 6
Edges 12

Q.

This cube has six faces and all of them are identical squares.If $x$ is the length of an edge of the cube, find the formula for the total length of all the edges of the cube.