Final answer:
The volume of the new cone is 1/a³ times the volume of the original cone.
Step-by-step explanation:
The volume of a cone is given by the formula V = 1/3 πr²h, where r is the radius and h is the height of the cone. If the original cone has a volume of 64 cubic feet, and the radius and height are reduced by a scale factor of a, then the new volume can be calculated by substituting the reduced values into the formula: Vnew = 1/3 π(r/a)²(h/a) = 1/3 πr²h/a³. Therefore, the volume of the new cone is 1/a³ times the volume of the original cone.
In this case, a is the scale factor by which the original cone is reduced. The volume of the new cone will be (1/a³) times 64 cubic feet. Since the scale factor is not specified in the question, we cannot determine the exact value of the volume of the new cone. Therefore, none of the provided statements accurately describe the volume of the new cone