Final answer:
To calculate the volume of the wedge, we determine that it represents 1/6 of the volume of the cylinder due to the 60° angle. Therefore, the volume of the wedge is 3π∙3 cubic units. The provided answer options do not match this calculation which suggests a possible error.
Step-by-step explanation:
To find the volume of a wedge cut out of a circular cylinder of radius 3 with one plane perpendicular to the axis and another intersecting it at a 60° angle along a diameter, we can use the formula for the volume of a cylinder V = πr²h, but we must adjust for the fact that the wedge represents only a portion of the cylinder. The full cylinder has a circular cross-section of radius 3, so its area is π(3^2) = 9π. The height of the cylinder is the same as the diameter, also 6 (since radius is 3). However, since the wedge is cut by a plane at a 60° angle, the proportion represented by the wedge is 1/6 of the full cylinder (because there are 360° in a circle, and 360°/60° = 6).
The volume of the wedge is therefore π(3^2)6 * (1/6) = 9π * 6 * (1/6) = 9π. This simplifies to 3π∙3, and since the exact value of π is approximately 3.14159, this gives us the volume of the wedge as 3∙3. Keeping π as a constant, we find that a = 3 and b = 3, but none of the options perfectly match this calculation. Therefore, there might be an error in the provided options or in the terms of the question as supplied. The exact volume of the wedge in terms of π can be expressed as 3π∙3 cubic units, not in the form of a∙√b as given in the options.