The Sphere of influence is the volume of soil throughout which the electrical potential rises to more than a small percentage of the potential rise of the ground electrode when that electrode discharges current into the soil.
The greater the volume compared with the volume of the electrode, the more efficient the electrode. For a more detailed answer read below or click play to watch our podcast on YouTube.

Elongated electrodes, such as ground rods, are the most efficient. The surface area of the electrode determines the ampacity of the device, but does not affect “the zone of influence”

Case in point, the greater the surface area, the greater the contact with the soil, and the more electrical energy that can be discharged per unit of time.

The formula for calculating the volume of soil is shown in Fig. 2 on the right above: A simpler version is used when the above formula is modified by rounding π (pi) down to 3 and cross canceling to get the formula: V=5L3 Thus, a single 10-foot driven rod will utilize 5,000 cubic feet of soil, whereas a single 8 foot rod will utilize about half the soil at 2,560 cubic feet. Going from 8 ft to 10 ft ground rod can provide a significant reduction in the resistance to ground as the sphere of influence  will be nearly doubled, given that the soil resistivity does not increase with depth. The Engineering Experts at E&S Grounding Solutions