Respuesta :
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.
#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.
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,
[tex]F+V=E+2[/tex]
Here [tex]F[/tex] is the number of faces, [tex]V[/tex] is the number of the vertex and [tex]E[/tex] 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,
[tex]\begin{aligned}\\ F+V&=E+2\\ F+6&=9+2\\ F&=11-6\\ F&=5\\ \end[/tex]
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,
[tex]\begin{aligned}\\F+V&=E+2\\25+V&=36+2\\V&=38-25\\V&=13\\\end[/tex]
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;
https://brainly.com/question/10732990
