Faces, Edges and Vertices

Q.

What is the shape of the face of a cube?

1. Rectangle

2. Square

3. Parallelogram

4. Rhombus

Q. Give examples of plane surfaces.

Q.

A hexagonal pyramid has ___ vertices.

1. 7

2. 5

3. 6

4. 8

Q. Which of the following is “Euler’s formula”?

1. E + F + 2 = V
2. E + F + 2 = V
3. E - F + V = 2
4. F - E + V = 2

Q.

Two dice are placed side by side with $4+2$, what is the total on the face opposite to the given numbers?

1. $6$
2. $8$
3. $7$
4. $9$

Q. Name a 3D solid having no faces, no edges and no vertices, justify your answer.

Q.

How many faces does a hexagonal prism have?

1. 6

2. 8

3. 10

4. 7

Q. What is the sum of the number of Faces, Vertices and Edges of a cube?

1. 20
2. 26
3. 18
4. 22

Q.

Question 76

Write the name of

a) vertices,

b) edges and

c) faces of the prism, shown in the given figure.

Q. Consider the figure (pyramid mounted over cube):

If the number of faces, number of edges and number of vertices be F, E and V respectively, then find the value of $F+E+V$.

1. $32$
2. $34$
3. $30$
4. $28$

Q.

Verify Euler's formula for the following solids. [4 MARKS]

Q.

Define vertex.

Q. What will be the number of edges in a polyhedron if there are 6 faces and 12 vertices?

1. 16
2. None of these
3. 12
4. 14

Q.

Every individual flat surface of a solid is called its vertex.

1. True

2. False

Q.

The corners of a solid shape are called its _________; the line segments of its skeleton are called its ___________; and its flat surfaces are its ________. The respective blanks should be filled by:

1. edges, faces, vertices

2. vertices, edges, faces

3. vertices, faces, edges

4. faces, edges, vertices

Q.

Write the number of faces, edges and vertices of a cube.

Q. If two regular tetrahedrons are stuck together along a common base, the number of edges in the new figure is .

1. 9
2. 12
3. 6

Q. Write the name of the:
a. vertices
b. edges and
c. faces of the prism shown in the figure.

[4 MARKS]

Q.

Consider the net figure of a rectangular pyramid:

Let the number of edges be E and number of vertices be V (in the 2-D figure: take edges as the intersection lines and vertices as intersection points of the lines).Then the value of E + V is 24. True/False?

1. False

2. True

Q. Fill in the blanks to make the following statements true:

(i) A cuboid has.... vertices.
(ii) A cuboid has.... edges.
(iii) a cuboid has .... faces.
(iv) The number of lateral faces of a cuboid is .....
(v) A cuboid all of whose edges are equal is called a....
(vi) Two adjacent faces of a cuboid meet in a line segment called its....
(vii) Each edge of a cuboid can be obtained as aline segment in which two... meet.
(viii) ....... edges of a cube (or cuboid) meet at each of its vertices.
(ix) A...... is a cuboid in which all the six faces are squares.
(x) The three concurrent edges of a cuboid meet at a point called the ..... of the cuboid.

Q. What will be the top view of the given solid whose base is a square?

1. Circle
2. Triangle
3. Rectangle
4. Square

Q.

In the figure of a cube,

i) Which edge is the intersection of faces EFGH and EFBA?
ii) Which faces intersect at edge FB?
iii) Which three faces from the vertex A?
iv) Which vertex is formed by the faces ABCD, ADHE and CDHG?
v) Give all the edges that are parallel to edge AB
vi) Give the edges that are neither parallel nor perpendicular to edge BC.
vii) Give all the edges that are perpendicular to edge AB.
viii) Give four vertices that do not all lie in one plane.

Q. Which of the following statements about a rectangular prism is not true?

1. There are 6 edges in a rectangular prism.
   
2. Volume of a rectangular prism $=l\times b\times h$
   
3. Opposite pairs of faces are identical in a rectangular prism.
   
4. Volume of a rectangular prism $=\text{base area}\times h$
   

Q.

Select the appropriate answer.

An edge is a

1. Line segment along which two adjacent faces meet.

2. the surface between two parallel faces of a cuboid.

3. Point where two faces meet.

Q.

Take two regular tetrahedrons and stick them along a common base. The number of edges in the new three dimensional shape formed are?

__

Q.

How many faces does a right rectangular prism have?

1. 6

2. 12

3. 5

4. 8

Q. How many edges does a triangular prism have ?

1. 12
2. 6
3. 9
4. 7

Q. Which of the following solids will have the given net?
(Note: A net diagram is a 2D plane figure that can be folded to form a 3D solid.)

1. Rectangular prism
   
2. Pyramid
   
3. Cone
   
4. Prism
   

Q. What is the number of faces and edges in a cube?

1. 6, 12
2. 6, 6
3. 12, 12
4. 12, 8

Q. Find the number of edges and vertices of the given figure.

1. edges = 12, vertices = 6
2. edges = 10, vertices = 12
3. edges = 6, vertices = 8
4. edges = 6, vertices = 12