Question

1. Two dice are placed side by side with 4+3, what is the total on the face opposite to the given
numbers
b) 7
c) 11
d) 6
(a) 3

2. What will be the number of faces if there are 6 vertices and 12 edges?
b)10
d) 18
(a) 8
c)12

3. What will be the number of edges if there are 12 vertices and 20 faces?
b)28
d)42
(a) 32
c)30
3. Which of the following is Euler's Formula:
(c)F-V=E-2
(bF +V=E-2
(dF- V + E =2
(a) F +V-E=2​

Answer 1

Answer:

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Step-by-step explanation:

a)Face opposite to 4 is 3 and opposite to 3 is 4

Therefore, there sum is equal to = 3 + 4 = 7

b)8

c)30 edges

d)F+V=E+2

Answer 2

Solution

1) The sum of numbers present on opposite sides of a dice is always 7.

So, number present on opposite face of 4 is 3.

Similarly, number present on opposite face of 3 is 4.

So, sum of numbers will be

3 + 4

7

So, answer is 7 which is option B.

2) Euler's formula for solids :

Vertices + Faces - Edges = 2

Vertex = 6

Edges = 12

Applying formula,

6 + Faces - 12 = 2

Faces = 12 - 6 + 2

Faces = 8

So, number of faces are 8 which is option A.

3) Vertex = 12

Faces = 20

Apply formula,

12 + 20 - Edges = 2

Edges = 32 - 2

Edges = 30

So, number of edges are 30 which is option C.

4) Correct formula of Euler's for solids is

Vertices + Faces - Edges = 2

V + F - E = 2

So, correct option is A.