1. What is the Cube Law?

The Cube Law describes how volume changes with scale factor changes. When an object is scaled by a factor k, its volume changes by k³. This principle is fundamental in physics, engineering, and biology.

2. How Does the Calculator Work?

The calculator uses the Cube Law equation:

Where:

• old V — Original volume (any units cubed)
• k — Scale factor (dimensionless)
• new V — Resulting volume (same units as old V)

Explanation: The cube law shows that volume scales with the cube of the linear dimensions. This has important implications for scaling physical systems.

3. Applications of the Cube Law

Details: The cube law is used in biomechanics (scaling animals), engineering (scaling prototypes), physics (scaling physical systems), and many other fields where size changes affect volume-dependent properties.

4. Using the Calculator

Tips: Enter the original volume and the scale factor. Both values must be positive numbers. The result will be in the same units as the original volume.

5. Frequently Asked Questions (FAQ)

Q1: Why does volume scale with the cube of the linear dimensions?
A: Because volume is three-dimensional (length × width × height), so when each dimension changes by factor k, the volume changes by k × k × k = k³.

Q2: What about surface area scaling?
A: Surface area scales with the square of the linear dimensions (k²), which leads to interesting consequences in biology and engineering.

Q3: Can this be used for non-cubic objects?
A: Yes, the cube law applies to any shape as long as all dimensions scale uniformly.

Q4: What are some real-world examples?
A: Giant ants in movies would collapse under their own weight (square-cube law), large ships need different proportions than small boats, and large animals have different bone proportions than small ones.

Q5: How does this relate to the square-cube law?
A: The square-cube law compares area (scaling with k²) to volume (scaling with k³), explaining why large and small versions of things can't be simply scaled copies.