2025 RI Promo Q1

A tablet is dissolving in water and is modelled as a cylinder, as shown in Fig. 1. At \(t\) seconds after being dropped into the water, the radius of the tablet is \(x\) mm, and its thickness is \(\frac{1}{3}x\) mm. The circular cross-sectional area of the tablet is decreasing at a constant rate of \(0.5\) mm\(^2\) per second. When \(x=5\), find the exact value of

1. \(\dfrac{\mathrm{d}x}{\mathrm{d}t}\),[2]
2. the rate of change of the volume of the tablet.[2]