Final answer:
The physical quantity R, calculated with the formula R = 4a²(b - c) where a, b, and c are distances, will have the SI unit of meters cubed (m³), as this formula represents a volume.
Step-by-step explanation:
The calculation of the physical quantity R is given by the formula R = 4a²(b - c). Since a, b, and c are distances measured in meters, we analyze the formula to find the SI unit for R. The squared term, a², has units of meters squared (m²), and (b - c) is a distance, so it has units of meters (m). When these are multiplied together, the resulting SI unit for R is meters cubed (m³), which corresponds to volume. Therefore, the correct answer is e. m³.