ANSWER
[tex] 18\pi\: cm^3/s[/tex]
STEP-BY-STEP EXPLANATION:
[tex] V= \frac {4}{3}\pi r^3\\\\
[/tex]
Differentiating with respect to t on both sides:
[tex] \frac{dV}{dt} = \frac {4}{3}\pi\times 3r^2\frac{dr}{dt} \\\\
\frac{dV}{dt} =4\pi r^2\frac{dr}{dt} .. (1)\\\\
Plug \:\frac{dr}{dt} = \frac{1}{2}\:\: \& \: \: r = 3\: in \: equation \: (1)\\\\
\frac{dV}{dt} =4\pi (3)^2\times \frac{1}{2}\\\\
\frac{dV}{dt} =4\pi\times 9\times \frac{1}{2}\\\\
\huge \purple {\boxed{\frac{dV}{dt} =18\pi\: cm^3/s}} \\[/tex]
