ecla7CubeDefinition:
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A cube is a three-dimensional shape with six square faces.
Properties:
- Faces: 6 squares of equal size
- Edges: 12 edges of equal length
- Vertices: 8 vertices
- Diagonals: 4 diagonals connecting opposite vertices
Dimensions:
- Length (L): The length of the sides of the squares
- Width (W): Same as length (L)
- Height (H): Same as length (L)
Volume:
Volume = L³Surface Area:
Surface Area = 6L²Diagonals:
- Body Diagonal: Connects two opposite vertices and passes through the center of the cube. Its length is √3 times the length of an edge (√3L).
Additional Information:
- A cube is a regular hexahedron.
- It is one of the five Platonic solids.
- A cube is a symmetrical shape with equal dimensions in all three directions.
- It can be inscribed in a sphere of radius L√2/2.
- It can be circumscribed around a sphere of radius L/2.
- A cube can be unfolded into a net that can be flattened into a plane.
- A cube is a common shape used in architecture, packaging, and other applications.Definition:
A cube is a three-dimensional shape with six square faces.
Key Features:
- Six square faces: All six faces are identical, forming a six-sided cube.
- Twelve edges: The intersections of the faces form twelve edges of equal length.
- Eight vertices: The points where the edges meet are called vertices (corners).
- Regular body: All sides and angles of a cube are equal, making it a regular polyhedron.
Dimensions and Volume:
- Length (L): The side length of the square faces.
- Volume (V): The space occupied by the cube, calculated as: V = L³
Surface Area:
- Surface area (A): The total area of the six square faces, calculated as: A = 6L²
Diagonal:
- Body diagonal: A line segment connecting two opposite vertices passes through the center of the cube. Its length is √3L.
Additional Facts:
- A cube is a special case of a rectangular prism where all dimensions are equal.
- It belongs to the Platonic solids, which are polyhedra with congruent regular faces.
- Cubes can be inscribed in a sphere and circumscribed around a sphere.
- It is used in various applications, such as packaging, architecture, and design.
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