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Volume of cone: \( V = \frac{1}{3}\pi r^2 h \); by similar triangles, \( r = \frac{5}{12}h \).
So \( V = \frac{1}{3}\pi \left(\frac{5}{12}h\right)^2 h = \frac{25\pi}{432} h^3 \).
Rate of change: \( \frac{dV}{dt} = -0.2\sqrt{h} \); but \( \frac{dV}{dt} = \frac{dV}{dh} \cdot \frac{dh}{dt} = \frac{25\pi}{432} \cdot 3h^2 \frac{dh}{dt} = \frac{25\pi}{144} h^2 \frac{dh}{dt} \).

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