Mathematics, 25.07.2019 08:00 VamPL

1. a polyhedron has 6 vertices and 9 edges. how many faces does it have? a. 3 b. 5 c. 7 d. 9 2. a polyhedron has 25 faces and 36 edges. how many vertices does it have? a. 11 b. 12 c. 13 d. 14 3. what is the cross section formed by a plane that contains a vertical line of symmetry for a tetrahedron? a. triangle b. square c. rectangle d. pentagon 4. what is the cross section formed by a plane that intersects three faces of a cube? a. triangle b. square c. rectangle d. pentagon

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Hello Madoudou!

#1

So we have:

F which is the number of faces we are looking for

E which are the numbers of edges

and V the number of vertices

We can use the Euler's polyhedron formula. Which is:

V - E + F = 2

Remember we are solving for F. Thus,

F = E - V + 2

F = 9 - 6 + 2

F = 9 - 4

F = 5

The correct answer is option B

#2

It is almost the same problem. They just want us to find the vertices.

V = E - F + 2

V = 36 - 25 + 2

V = 36 - 23

V = 13

The correct answer is option C

#3

The cross section formed by a plane that contains a vertical line of symmetry for a tetrahedron is a Triangle.

The correct answer is option A

#4

The cross section formed by a plane that intersects three faces of a cube is a Triangle.

The correct answer is option A

Let me know if you have any questions about the answers. As always, it is my pleasure to help students like you.

Answer from: nyceastcoast

Polyhedron is three-dimensional solid which consist collection of polygons joint with edges.

The option B is the correct option for problem 1.The option C is the correct option for problem 2.The option A is the correct option for problem 3.The option A is the correct option for problem 4.

Polyhedron

Polyhedron is three-dimensional solid which consist collection of polygons joint with edges.

The Euler's formula between the vertex, edges and faces can be given as,

F+V=E+2

Here is the number of faces, is the number of the vertex and is the number of edges of the polyhedron.

1) The polyhedron which has 6 vertices and 9 edges,

Use the Euler's formula to find the faces as,

$\begin{aligned}\\
F+V&=E+2\\
F+6&=9+2\\
F&=11-6\\
F&=5\\
\end$

Thus the polyhedron which has 6 vertices and 9 edges has 5 number of faces. The option B is the correct option for problem 1.

2) The polyhedron which has 25 faces and 36 edges,

Use the Euler's formula to find the faces as,

$\begin{aligned}\\F+V&=E+2\\25+V&=36+2\\V&=38-25\\V&=13\\\end$

Thus the polyhedron which has 25 faces and 36 edges has 13 number of vertex. The option C is the correct option for problem 2.

3) The cross section formed by a plane that contains a vertical line of symmetry for a tetrahedron-

Tetrahedron is a triangular pyramid with four triangular faces. Thus The cross section formed by vertical line contained plane of symmetry for a tetrahedron is triangle. Thus The option A is the correct option for problem 3.

4) The cross section formed by a plane that intersects three faces of a cube-

When a plane intersect the cube with three of its faces the cross section of that plane is a triangle. Thus The option A is the correct option for problem 4.

Hence,

The option B is the correct option for problem 1.The option C is the correct option for problem 2.The option A is the correct option for problem 3.The option A is the correct option for problem 4.

Learn more about the polyhedron here;

link

Answer from: Quest

However, if the workers do outside of what's normally expected, go ahead and tip.

Answer from: Quest

what? that isnt a question

step-by-step explanation: