how many vertices ,edges and faces will a cuboid have ? what is the shape of its faces
The correct answer and explanation is:
A cuboid has:
- Vertices: 8
- Edges: 12
- Faces: 6
- Shape of its faces: Rectangles
Explanation:
A cuboid is a three-dimensional solid object bounded by six rectangular faces. It is also known as a rectangular prism. To understand its structure, it helps to break down the geometry:
Vertices:
A vertex is a point where edges meet. In a cuboid, each corner where three edges intersect forms a vertex. There are 4 vertices on the top face and 4 on the bottom face, totaling 8 vertices.
Edges:
An edge is a line segment that connects two vertices. Each face of the cuboid is a rectangle, and each rectangle has 4 edges. Although there are 6 faces, edges are shared between faces. The total unique edges are:
- 4 on the top face
- 4 on the bottom face
- 4 vertical edges connecting top and bottom
This results in 12 edges in total.
Faces:
The cuboid has 6 faces:
- 2 opposite top and bottom faces
- 2 opposite left and right side faces
- 2 opposite front and back faces
All six faces are rectangular in shape. In a special case where all faces are squares (all sides equal), the cuboid becomes a cube. But generally, in a cuboid, opposite faces are equal rectangles.
Shape of Faces:
Each face of a cuboid is a rectangle. These rectangles may not all be identical, but opposite faces are always congruent. For example, the front and back are equal in size, the top and bottom are equal, and the left and right sides are equal.
In summary, a cuboid has 8 vertices, 12 edges, and 6 rectangular faces. Its shape is based on right angles and straight lines, making it one of the simplest and most recognizable 3D shapes in geometry.