Final answer:
The volume of the cone with the same base area and height as the given cylinder with a volume of 215π cubic units is 71.67π cubic units or approximately 225 cubic units when rounded to the nearest whole number.
Step-by-step explanation:
The volume V of a cylinder is calculated by the formula V = πr²h, where r is the radius of the cylinder's base and h is its height.
For a cone with the same base area and height as the cylinder, its volume V_c is one third of the cylinder's volume. Since the given volume of the cylinder is 215π cubic units, the volume of the cone would be 215π / 3 cubic units, which simplifies to 71.67π cubic units.
When using π as 3.14, the volume of the cone is approximately 225 cubic units when rounded to the nearest whole number.