Differentiation

Differentiation

Secondary 4

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:

  1. \(\dfrac{\mathrm{d}V}{\mathrm{d}r}\);

  2. \(\dfrac{\mathrm{d}V}{\mathrm{d}t}\), including units.

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Answer:\(\frac{\mathrm{d}V}{\mathrm{d}r}=36\pi\text{ cm}^2;\frac{\mathrm{d}V}{\mathrm{d}t}=\frac{36\pi}{5}\text{ cm}^3/\text{s}\).

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