Volume of Cube Calculator 2025: Complete Guide (1000+ Words)
A cube is the most symmetric 3D shape with all sides equal. Our 2025 Volume of Cube Calculator computes volume, surface area, space diagonal, and face diagonal from side length with full step-by-step explanations.
What is a Cube?
A cube has 6 square faces, 12 edges, and 8 vertices. All edges are equal.
- Side length (a): Length of one edge
- Volume (V): Space inside
- Surface Area (SA): Total face area
- Space Diagonal: From one vertex to opposite
Core Formulas
Volume: V = a³
Surface Area: SA = 6a²
Face Diagonal: d = a√2
Space Diagonal: s = a√3
Surface Area: SA = 6a²
Face Diagonal: d = a√2
Space Diagonal: s = a√3
Example: Side = 5 cm
V = 5³ = 125 cm³
SA = 6 × 5² = 150 cm²
Face diagonal = 5√2 approximately 7.071 cm
Space diagonal = 5√3 approximately 8.660 cm
SA = 6 × 5² = 150 cm²
Face diagonal = 5√2 approximately 7.071 cm
Space diagonal = 5√3 approximately 8.660 cm
Applications
- Packaging: Boxes, containers
- Construction: Concrete blocks, bricks
- Science: Crystal structures, unit cells
- Storage: Ice cubes, dice
Step-by-Step: Side = 8 m
V = 8³ = 512 m³
SA = 6 × 64 = 384 m²
Space diagonal = 8√3 approximately 13.856 m
Common Mistakes
- Using a² instead of a³ for volume
- Forgetting factor of 6 in surface area
- Confusing face and space diagonal
Advanced: Cube in Coordinate Geometry
Vertices at (0,0,0) to (a,a,a)
Related Tools
FAQs
Can a cube have zero volume? Only if side = 0 (degenerate).
Is a cube a regular polyhedron? Yes, all faces are regular polygons.
Conclusion
Cubes are foundational in 3D geometry. Our 2025 Volume of Cube Calculator delivers instant precision with crystal-clear steps. Master cubic geometry today!
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