詳解：(1)建立函數關係式， \(V\) 表氣球體積， \(r\) 表半徑

\(\begin{array}{l}V = \frac{4}{3}\pi  \cdot {r^3}\\\end{array}\)

(2)依照題意條件

\(\frac{{dV}}{{dt}} = 9\)，\(r = 3\)，欲求 \(\frac{{dr}}{{dt}}\)=?

(3)函數關係式對 \(t\) 微分

\(\frac{{dV}}{{dt}} = \frac{4}{3}\pi  \cdot 3{r^2}\frac{{dr}}{{dt}}\)\(\begin{array}{l} \Rightarrow 9 = \frac{4}{3}\pi  \cdot 3 \cdot 9\frac{{dr}}{{dt}}\\\end{array}\)

\(\begin{array}{l}\frac{{dr}}{{dt}} = \frac{1}{{4\pi }}\\\end{array}\)

故選(A)