When an isosceles right triangle with legs measuring 4 inches is rotated about one of its legs, it forms a cone. The leg around which it is rotated serves as the height of the cone, and the other leg becomes the radius of the base of the cone.
In this case, the height of the cone is 4 inches (the length of the leg being rotated about), and the radius of the base is also 4 inches (the length of the other leg).
Since the diameter of a circle is twice the radius, the diameter of the base of the cone formed is:
Diameter = 2 × radius = 2 × 4 inches = 8 inches.
Thus, the correct response is:
cone with a diameter of 8 inches.