Volume of a Cube Calculator

Surface Area

Surface Area (cm²): Surface Area (m²): Surface Area (in²): Surface Area (ft²):

Cube Diagonal \( d \)

Cube Diagonal (cm): Cube Diagonal (m): Cube Diagonal (in): Cube Diagonal (ft):

Face Diagonal \( f \)

Face Diagonal (cm): Face Diagonal (m): Face Diagonal (in): Face Diagonal (ft):

Volume

Volume (cm³): Volume (m³): Volume (in³): Volume (ft³): Volume (liters):

1. What is a Volume of a Cube Calculator?

Definition: This calculator computes the volume, surface area, cube diagonal, and face diagonal of a cube based on its side length (\( a \)).

Purpose: Useful in geometry, engineering, and everyday applications for determining the properties of cube-shaped objects (e.g., boxes, dice).

2. How Does the Calculator Work?

The calculations are based on the following formulas:

\[ V = a^3 \] \[ \text{Surface Area} = 6 \times a^2 \] \[ d = a \times \sqrt{3} \] \[ f = a \times \sqrt{2} \]

Unit Conversions:

Input (Length): mm (×0.1), cm (×1), m (×100), in (×2.54), ft (×30.48) to cm
Volume (from cm³): m³ (×0.000001), in³ (×0.0610237), ft³ (×0.0000353147), liters (×0.001)
Surface Area (from cm²): m² (×0.0001), in² (×0.155), ft² (×0.00107639)
Length (from cm): m (×0.01), in (×0.393701), ft (×0.0328084)

Explanation: The side length is converted to cm, the volume, surface area, cube diagonal, and face diagonal are calculated, and then converted to other units.

3. Importance of Cube Volume Calculation

Details: Calculating the volume, surface area, and diagonals of a cube is essential in packaging, construction, and storage for determining capacity and structural properties.

4. Using the Calculator

Tips: Enter the side length \( a \) in mm, cm, m, in, or ft (must be >0). The result shows the side length, surface area, cube diagonal, and face diagonal in cm, m, in, and ft, and the volume in cm³, m³, in³, ft³, and liters.

5. Example

Given: Side length \( a = 25 \, \text{cm} \).
Volume Calculation: \( V = 25^3 = 15,625 \, \text{cm}^3 \).
Surface Area Calculation: \( \text{Surface Area} = 6 \times 25^2 = 3,750 \, \text{cm}^2 \).
Cube Diagonal Calculation: \( d = 25 \times \sqrt{3} \approx 43.301 \, \text{cm} \).
Face Diagonal Calculation: \( f = 25 \times \sqrt{2} \approx 35.355 \, \text{cm} \).
Conversions (Side Length):
- \( \text{cm} = 25 \),
- \( \text{m} = 0.25 \),
- \( \text{in} \approx 9.843 \),
- \( \text{ft} \approx 0.82 \).
Conversions (Surface Area):
- \( \text{cm}^2 = 3,750 \),
- \( \text{m}^2 = 0.375 \),
- \( \text{in}^2 \approx 581.25 \),
- \( \text{ft}^2 \approx 4.036 \).
Conversions (Cube Diagonal):
- \( \text{cm} \approx 43.301 \),
- \( \text{m} \approx 0.433 \),
- \( \text{in} \approx 17.047 \),
- \( \text{ft} \approx 1.421 \).
Conversions (Face Diagonal):
- \( \text{cm} \approx 35.355 \),
- \( \text{m} \approx 0.354 \),
- \( \text{in} \approx 13.919 \),
- \( \text{ft} \approx 1.16 \).
Conversions (Volume):
- \( \text{cm}^3 = 15,625 \),
- \( \text{m}^3 = 0.015625 \),
- \( \text{in}^3 \approx 953.495 \),
- \( \text{ft}^3 \approx 0.551 \),
- \( \text{liters} \approx 15.625 \).

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