In the explosive behavior model, the volume is raised to which power?

In the explosive behavior model, the volume is raised to which power?

• A. 1/3
• B. 1/2
• C. 2/3
• D. 1

Answer: (A)

In this model a length scale drives the expansion, and for a spherical region the volume scales with the radius cubed. Since V ∝ r^3, the radius r is proportional to the cube root of the volume, r ∝ V^(1/3). Using V^(1/3) to describe the growth links the volume change to a linear dimension that governs how the explosion front propagates. The other powers don’t match the geometry: 2/3 corresponds to surface area scaling, 1/2 has no direct geometric basis here, and 1 would imply a linear relation with volume that isn’t consistent with a sphere’s volume-growth relationship.

In this model a length scale drives the expansion, and for a spherical region the volume scales with the radius cubed. Since V ∝ r^3, the radius r is proportional to the cube root of the volume, r ∝ V^(1/3). Using V^(1/3) to describe the growth links the volume change to a linear dimension that governs how the explosion front propagates. The other powers don’t match the geometry: 2/3 corresponds to surface area scaling, 1/2 has no direct geometric basis here, and 1 would imply a linear relation with volume that isn’t consistent with a sphere’s volume-growth relationship.