Cube Calc: find V, a, d
Find Volume (V), side length (a), space diagonal (d), and all cube properties from any known parameter
Calculate Cube Properties
Cube Properties: V, a, d
Calculation Steps
Given: Side Length (a) = 0 cm
Step 1: Calculate side length: a = 0.0000 cm
Step 2: Volume: V = a³ = 0.0000 cm³
Step 3: Space diagonal: d = a√3 = 0.0000 cm
Step 4: Surface area: S = 6a² = 0.0000 cm²
Step 5: Face diagonal: f = a√2 = 0.0000 cm
Formula used: V = a³, d = a√3, S = 6a², f = a√2
Example Calculations
Example 1: Given side length a = 5 cm
Given: Side length a = 5 cm
Volume: V = a³ = 5³ = 125 cm³
Space diagonal: d = a√3 = 5 × √3 = 8.66 cm
Surface area: S = 6a² = 6 × 5² = 150 cm²
Face diagonal: f = a√2 = 5 × √2 = 7.07 cm
Example 2: Given volume V = 64 cm³
Given: Volume V = 64 cm³
Side length: a = ∛V = ∛64 = 4 cm
Space diagonal: d = a√3 = 4 × √3 = 6.93 cm
Surface area: S = 6a² = 6 × 4² = 96 cm²
Face diagonal: f = a√2 = 4 × √2 = 5.66 cm
Key Formulas Summary
Volume: V = a³
Side from Volume: a = ∛V
Space Diagonal: d = a√3
Side from Diagonal: a = d/√3
Surface Area: S = 6a²
Side from Surface: a = √(S/6)
Face Diagonal: f = a√2
Side from Face Diagonal: a = f/√2
Parameter Definitions
Side Length (a)
Length of any edge of the cube
Volume (V)
Amount of space inside the cube
Space Diagonal (d)
Diagonal through the cube's interior
Surface Area (S)
Total area of all six faces
Face Diagonal (f)
Diagonal across any square face
Calculation Methods
From Side Length
Direct calculation of all properties
From Volume
Find side using cube root: a = ∛V
From Space Diagonal
Use relationship: a = d/√3
From Surface Area
Calculate: a = √(S/6)
From Face Diagonal
Use relationship: a = f/√2
Applications
Packaging and shipping calculations
Dice and gaming cube design
Storage container optimization
Architecture and construction
Material science calculations
Understanding Cube Calculations: V, a, d
Core Relationships
This calculator focuses on the three fundamental properties of a cube: Volume (V), side length (a), and space diagonal (d). These properties are interconnected through specific mathematical relationships that allow us to calculate any property from any other.
Key Formulas
- •Volume: V = a³ (side cubed)
- •Space Diagonal: d = a√3 (side times √3)
- •Surface Area: S = 6a² (bonus calculation)
- •Face Diagonal: f = a√2 (bonus calculation)
Reverse Calculations
From Volume to Side: a = ∛V
From Space Diagonal to Side: a = d/√3
From Surface Area to Side: a = √(S/6)
From Face Diagonal to Side: a = f/√2
Mathematical Note: The space diagonal formula d = a√3 comes from applying the Pythagorean theorem twice: first to find the face diagonal (a√2), then to find the space diagonal √((a√2)² + a²) = √(3a²) = a√3.