A spherical balloon has radius \(r\) cm and volume\[V=\frac43\pi r^3.\] Its radius increases at \(0.2\text{ cm/s}\).
When \(r=3\), find:
\(\dfrac{\mathrm{d}V}{\mathrm{d}r}\);
\(\dfrac{\mathrm{d}V}{\mathrm{d}t}\), including units.
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