FACES EDGES AND VERTICES WORKSHEET

Question 1 :

In a 3-D shape, what are faces, edges and vertices?

Solution :

A cube. A cube is made of six square shaped planes. These 6 square shaped planes of the cube are known as its faces.

A line segment which connects any two faces of a cube is called as Edge and each corner point where three edges meet is called as Vertex. So, a cube has 6 faces, 12 edges and 8 vertices.

Question 2-6 : Name and write the number of faces (F), vertices (V) and edges (E) for the following polyhedrons. Also find F + V – E.

Question 2 :

Solution :

Name : Cube

Face : 6

Vertices : 8

Edges : 12

F + V - E = 6 + 8 - 12 = 2

Question 3 :

Solution :

Name : Cuboid

Face : 6

Vertices : 8

Edges : 12

F + V - E = 6 + 8 - 12 = 2

Question 4 :

Solution :

Name : Triangular Prism

Face : 5

Vertices : 6

Edges : 9

F + V - E = 5 + 6 - 9 = 2

Question 5 :

Solution :

Name : Square Pyramid

Face : 5

Vertices : 5

Edges : 8

F + V - E = 5 + 5 - 8 = 2

Question 6 :

Solution :

Name : Triangular Pyramid

Face : 4

Vertices : 4

Edges : 6

F + V - E = 4 + 4 - 6 = 2

Question 7 :

What do you observe from the answers of the above questions 2 to 6?

Solution :

We observe that, F + V – E = 2 in all the cases.

This is true for any polyhedron and this relation

F + V – E = 2

is known as Euler’s formula.

Question 8 :

Choose the attributes of the shape.

Cube

a)  6 flat surfaces

b)  12 vertices

c)  12 edges

d)  edges of equal length

Solution :

Cube will have 6 faces, 8 vertices and 12 edges. Each face of cube is square, so all sides will be equal.

Options a, c and d are correct.

Question 9 :

I am a three-dimensional shape that has no flat surfaces, no vertices, and no edges. What am I?

Solution :

Number of flat faces = 0

Number of vertices = 0

Number of edges = 0

The shape must be a circle.

Question 10 :

I am a three-dimensional shape that has 1 flat surface, 1 vertex, and one edge. What am I?

Solution :

Number of flat faces = 1

Number of vertex = 1

Number of edges = 1

The shape must be a cone.

Question 11 :

Newton buys an item that has 2 more flat surfaces than vertices. Which item does he buy?

Solution :

• Sphere has no flat surface.
• The cylinder has two flat face, at the top and bottom.
• The cube has 6 flat faces.

Question 12 :

Circle the object below the table that has 0 flat surfaces. Draw a line through the object above the basketball that has 12 straight edges.

Solution :

Number of flat surfaces :

• Globe and spherical ball are 0 flat surfaces.
• For the tissue holder, it has 12 edges.

Question 13 :

Choose the attributes of the shape.

Rectangular prism

a)  6 flat surfaces

b)  12 vertices

c)  12 edges

d)  Two dimensional

Solution :

The rectangular prism will have

• 6 faces, each will be in the shape of rectangle.
• 8 vertices
• 12edges
• It it three dimensional shape.

So, options a and c are the attributes for the shape rectangular prism.

Question 14 :

Choose the attributes of the shape.

Sphere

a)  0 flat surfaces

b)  1 flat surfaces

c)  0 edges

d)  rolls

Solution :

In sphere,

• there is no flat surface
• no edges, because it is not created by straight lines.
• rolls, yes it has roll.

So, options a, c and d are correct.

Question 15 :

How many of each shape make up the playground tunnels?

a) ____ cube

b) _____ rectangular prism

c) _____cylinders

d) _____cone

e) ______sphere

Solution :

a) Number of cube is 1

b) Number of rectangular prism is 1.

c) Number of cylinders are 3.

d) Number of cone is 1

e) Number of sphere is 1

Question 16 :

What is the name given to a solid object that has a curved surface and two circular ends?

A) Sphere    B) Cone      C) Cylinder

Solution :

In cylinder, at the top and at the bottom we have two flat circular faces and around the figure we have curved surfaces.

So, the answer is cylinder.

Question 17 :

Baked beans usually come in what shaped cans?

A) Square     B) Cylindrical      C) Cubed

Solution :

The shape is cylinder.

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