1. The problem asks to identify which graph represents a function that is periodic and sinusoidal, and then to find the diameter of the Ferris wheel based on the height graph. 2. A sinusoidal function is a smooth, periodic wave that can be modeled by sine or cosine functions. It oscillates regularly above and below a central axis. 3. From the descriptions: - (A) is a parabola, not periodic. - (B) is a zigzag, periodic but not sinusoidal. - (C) is a smooth sinusoidal wave, periodic and sinusoidal. - (D) is periodic but not smooth sinusoidal. Therefore, graph (C) represents a periodic and sinusoidal function. 4. For the Ferris wheel height $h(t)$, the diameter is the total vertical distance covered by the wheel, which equals the difference between the maximum and minimum heights. 5. Since the graph is sinusoidal, the height function can be modeled as: $$h(t) = A \sin(\omega t) + D$$ where $A$ is the amplitude (half the diameter), and $D$ is the vertical shift (center height). 6. The diameter $d$ is twice the amplitude: $$d = 2A = \text{max height} - \text{min height}$$ 7. From the sinusoidal graph (C), the maximum height minus the minimum height gives the diameter of the Ferris wheel. Final answer: - The graph representing a periodic and sinusoidal function is (C). - The diameter of the Ferris wheel is the vertical distance between the maximum and minimum heights on the graph, i.e., $d = \text{max height} - \text{min height}$ metres.