How many faces, edges, and vertices are there in a cube

How many faces, edges, and vertices are there in a cube? 2. How many faces, edges, and vertices are there in a cuboid? 3. How many faces, edges, and vertices are there in a sphere? 4. How many faces, edges, and vertices are there in a cylinder? 5. How many faces, edges, and vertices are there in a cone? 6. How many faces, edges, and vertices are there in a triangular pyramid? 7. How many faces, edges, and vertices are there in a square pyramid? 8. How many faces, edges, and vertices are there in a pentagonal pyramid? 9. How many faces, edges, and vertices are there in an octagonal pyramid? 10. How many faces, edges, and vertices are there in a triangular prism? 11. How many faces, edges, and vertices are there in a pentagonal prism? 12. How many faces, edges, and vertices are there in a hexagonal prism? 13. How many faces, edges, and vertices are there in an octagonal prism?

1. How many faces, edges, and vertices are there in a cube? 2. How many faces, edges, and vertices are there in a cuboid? 3. How many faces, edges, and vertices are there in a sphere? 4. How many faces, edges, and vertices are there in a cylinder? 5. How many faces, edges, and vertices are there in a cone? 6. How many faces, edges, and vertices are there in a triangular pyramid? 7. How many faces, edges, and vertices are there in a square pyramid? 8. How many faces, edges, and vertices are there in a pentagonal pyramid? 9. How many faces, edges, and vertices are there in an octagonal pyramid? 10. How many faces, edges, and vertices are there in a triangular prism? 11. How many faces, edges, and vertices are there in a pentagonal prism? 12. How many faces, edges, and vertices are there in a hexagonal prism? 13. How many faces, edges, and vertices are there in an octagonal prism?

The Correct Answer and Explanation is:

Here are the correct numbers of faces, edges, and vertices for each of the listed three-dimensional shapes:

1. Cube:
   Faces: 6
   Edges: 12
   Vertices: 8
2. Cuboid:
   Faces: 6
   Edges: 12
   Vertices: 8
3. Sphere:
   Faces: 0
   Edges: 0
   Vertices: 0
4. Cylinder:
   Faces: 3 (2 circular, 1 curved surface)
   Edges: 2 (curved edge where each circle meets the curved surface)
   Vertices: 0
5. Cone:
   Faces: 2 (1 circular base, 1 curved surface)
   Edges: 1 (around the circular base)
   Vertices: 1 (at the tip or apex)
6. Triangular Pyramid (Tetrahedron):
   Faces: 4
   Edges: 6
   Vertices: 4
7. Square Pyramid:
   Faces: 5
   Edges: 8
   Vertices: 5
8. Pentagonal Pyramid:
   Faces: 6
   Edges: 10
   Vertices: 6
9. Octagonal Pyramid:
   Faces: 9
   Edges: 16
   Vertices: 9
10. Triangular Prism:
    Faces: 5
    Edges: 9
    Vertices: 6
11. Pentagonal Prism:
    Faces: 7
    Edges: 15
    Vertices: 10
12. Hexagonal Prism:
    Faces: 8
    Edges: 18
    Vertices: 12
13. Octagonal Prism:
    Faces: 10
    Edges: 24
    Vertices: 16

Explanation

In geometry, three-dimensional shapes are classified based on their faces (flat surfaces), edges (line segments where faces meet), and vertices (corners where edges meet). A cube and cuboid both have six faces, all of which are rectangles or squares. They also share the same number of edges and vertices. A sphere is smooth with no flat surface or corner, so it lacks faces, edges, and vertices.

A cylinder has two flat circular faces and a curved surface that connects them. It has two edges where the circles meet the curved face, but no corners. A cone is similar but has only one flat circular face and one curved surface, along with a single vertex at its apex.

Pyramids have a polygon base and triangular faces that meet at the apex. The number of faces, edges, and vertices depends on the base. A triangular pyramid (tetrahedron) has three triangular sides and one base. As the number of sides in the base increases, so do the total number of faces, edges, and vertices.

Prisms are solid figures with two identical polygonal bases and rectangular side faces. A triangular prism has two triangular bases, a pentagonal prism has two pentagonal bases, and so on. The number of faces equals the number of base sides plus two. Edges and vertices follow predictable patterns based on doubling the base’s characteristics and adding the connecting sides.

Understanding these properties helps in visualizing and constructing 3D shapes and supports deeper learning in geometry.