A tablet is dissolving in water. The tablet is modelled as a cylinder, shown in Figure 1. At $$\(t\)$$ seconds after the tablet is dropped into the water, the radius of the tablet is $$\(x \mathrm{~mm}\)$$ and the length of the tablet is $$\(3 x \mathrm{~mm}\)$$. The cross-sectional area of the tablet is decreasing at a constant rate of $$\(0.5 \mathrm{~mm}^{2} \mathrm{~s}^{-1}\)$$ (a) Find $$\(\frac{\mathrm{d} x}{\mathrm{~d} t}\)$$ when $$\(x=7\)$$ (4) (b) Find, according to the model, the rate of decrease of the volume of the tablet when $$\(x=4\)$$ (4)

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