Exam Question

### (a) Metacentric Diagram for a Vessel of Constant Triangular Cross-Section
A metacentric diagram is a graphical representation of a vessel's key stability parameters plotted against its draught. For a vessel with a constant triangular cross-section (apex down), the characteristics of the curves are as follows:
* **Axes**: The vertical axis represents height above the keel (K) in meters, and the horizontal axis represents the vessel's draught (d) in meters.
* **Curve of KG**: For a body of uniform density, the centre of gravity (G) is at a fixed position, which is the geometric centre of the entire body. For a triangle with total depth D, KG is constant and located at a height of $$\frac{2}{3}D$$ from the apex (keel). Therefore, the KG curve is a horizontal straight line on the diagram.