What shape is displayed by a vessel proceeding under sail while also being propelled by machinery?

The correct answer is the conical shape, which is displayed by a vessel that is under sail and also being propelled by machinery. According to the COLREGs (International Regulations for Preventing Collisions at Sea), specifically in Rule 25 regarding sailing vessels, a vessel that is under both sail and power is required to exhibit a conical shape, which is a black conical shape with the apex pointing upwards. This is a critical indicator for other vessels to recognize the operational state of the boat.

In terms of identification and navigation safety, the shape helps to communicate to other vessels that the ship is not solely a sailing vessel; rather, it is utilizing its mechanical propulsion as well. This distinction is important for the navigation and safety of all vessels in the area.

Other choices do not align with the conventions laid out by the COLREGs. For example, a cylinder shape or a square shape would not convey the necessary information about a vessel's operational status, and three shapes in a vertical line do not correspond to any recognized display for a sailing vessel using machinery.