計算6另解
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\( \displaystyle V=\frac{\pi r^2 h}{3}=\frac{\pi \left( \displaystyle \frac{h}{2} \right)^2 h}{3}=\frac{\pi h^3}{12}=3 t \)
\( \displaystyle \Rightarrow t=\frac{\pi h^3}{36} \)
\( \displaystyle \Rightarrow \frac{dh}{dt}=\frac{1}{\displaystyle \frac{dt}{dh}}=\frac{1}{\displaystyle \frac{\pi h^2}{12}}=\frac{12}{\pi h^2}|_{h=3}=\frac{12}{\pi \times 9}=\frac{4}{3 \pi} \)
