Answer
(a) $14.4\pi$
(b) $2.304\pi$
Work Step by Step
Given $ r= 0.4t $, since $V= \dfrac{4}{3}\pi r^3$, then
\begin{align*}
\frac{d V}{d t}&=\frac{d V}{d r} \frac{d r}{d t}\\
&=( 4 \pi r^{2}) \cdot(0.4)\\
&=1.6 \pi r^{2}
\end{align*}
(a) For $r= 3$, we get
\begin{align*}
\frac{d V}{d t}\bigg|_{r=3} &=1.6 \pi (3)^{2}\\
&= 14.4\pi
\end{align*}
(b) For $t= 3$, we have $r= 1.2$
\begin{align*}
\frac{d V}{d t}\bigg|_{t=3} &=1.6 \pi (1.2)^{2}\\
&= 2.304\pi
\end{align*}
