In the explosive data equation, the volume exponent is what?

• A. 2/3
• B. 1/3
• C. 1/2
• D. 1

Answer: (B)

In three-dimensional space, volume scales with the cube of a characteristic length. If you call that length L, then volume V is proportional to L^3. So to get a length from a volume, you take the cube root: L ∝ V^(1/3). That cube-root relationship is the volume exponent.

This is why the volume exponent is 1/3: it reflects how volume grows as you scale linear dimensions, and how you reverse that scaling to obtain a length from a given volume. Doubling the length increases volume by a factor of eight (since 2^3 = 8), while taking the cube root of a volume brings you back to the original length. The other exponents don’t match the fundamental 3D scaling of volume, so they don’t fit the typical volume-to-length relationship.