Final answer:
The Romans replaced cut stone with concrete in their building design, which was a cheaper and lighter material. They perfected the recipe for concrete by mixing water, lime, and pozzolana, volcanic ash. Concrete allowed them to build taller and more complicated structures efficiently.
Step-by-step explanation:
The Roman invention in building design that replaced cut stone was concrete. Concrete was a cheaper and lighter material than most other stones used for construction. The Romans perfected the recipe for concrete during the third century BCE by mixing together water, lime, and pozzolana, volcanic ash mined from the countryside surrounding Mt. Vesuvius. With concrete, the Romans were able to build taller, more complicated structures quickly and efficiently.