The volume of the cone is 648 cubic units. Hence the correct option is c.
The formula for the volume of a cone is derived from the formula for the volume of a cylinder, considering that a cone can be thought of as one-third of a cylinder with the same base and height. In this case, the given diameter of the cone is used to find the radius, which is crucial in calculating the volume.
The radius (r) is determined by dividing the diameter by 2, giving us 9 units. The height (h) is provided as 8 units. Plugging these values into the volume formula V = (1/3)πr²h, we obtain V = (1/3)π(9²)(8) = 648 cubic units.
Therefore, the volume of the cone with a diameter of 18 units and a height of 8 units is 648 cubic units. This calculation showcases the fundamental principles of geometry and demonstrates how to apply them in determining the volume of a cone. Hence the correct option is c.