When an isosceles right triangle with legs measuring 4 inches is rotated about one of its legs, it forms a cone. The leg that is used as the axis of rotation remains stationary, while the other leg sweeps out a circular shape, forming the base of the cone.
The diameter of the cone's base corresponds to the length of the leg perpendicular to the axis of rotation. Since the other leg also measures 4 inches, this means that the base of the cone has a diameter of 4 inches.
Thus, the correct response is:
cone with a diameter of 4 inches.