Differentiation

A spherical object shrinks while remaining spherical.
Its volume and surface area are
\[V=\frac43\pi r^3, \qquad S=4\pi r^2.\] Its volume satisfies \[\frac{\mathrm{d}V}{\mathrm{d}t}=-kS,\] where \(k=0.02\text{ cm/s}\).

1. Show that \(\dfrac{\mathrm{d}r}{\mathrm{d}t}=-k\), for \(r>0\).

2. Find \(\dfrac{\mathrm{d}S}{\mathrm{d}t}\) when \(r=5\text{ cm}\).

3. Is the volume decreasing at a constant rate? Explain.