Question

Use Euler's formula to determine the missing quantity.

Answer 1

Answer with step-by-step explanation:

The Euler's formula is given by V − E + F = 2 where V = number of vertices, E - number of edges and F = number of faces.

Substituting the given values for each shape to find the missing value.

1. Triangular prism: 6 - E + 5 = 2, E = 9

2. Rectangular prism: 8 - 12 + F = 2. F = 6

3. Pentagonal prism: V - 15 + 7 = 2, V = 10

4. Octagonal prism: 16 - E + 10 = 2, E = 24

5. Triangular pyramid: V - 6 + 4 = 2, V = 4

6. Rectangular pyramid: 5 - 8 + F = 2, F = 5

7. Pentagonal pyramid: 6 - E + 6 = 2, E = 10

Answer 2

Triangular prism has 9 edges

Rectangular prism has 6 faces

Pentagonal prism has 10 vertices

Hexagonal prism has 8 faces

Octagonal prism has 24 edges

Triangular pyramid has 4 vertices

Rectangular pyramid has 5 faces

Pentagonal pyramid has 10 edges

Explanation:

Use euler's formula V - E + F = 2

6 - E + 5 = 2 ⇒ E = 6 + 5 - 2 = 9

8 - 12 + F = 2 ⇒ F = 2 - 8 + 12 = 6

V - 15 + 7 = 2 ⇒ V = 2 + 15 - 7 = 10

12 - 18 + F = 2 ⇒ F = 2 - 12 + 18 = 8

16 - E + 10 = 2 ⇒ E = 16 + 10 - 2 = 24

V - 6 + 4 = 2 ⇒ V = 2 + 6 - 4 = 4

5 - 8 + F = 2 ⇒ F = 2 - 5 + 8 = 5

6 - E + 6 = 2 ⇒ E = 6 + 6 - 2 = 10