Answer
\begin{equation}
\frac{d V}{d t}=\frac{\ln 2}{20} V(t)
\end{equation}
Work Step by Step
\begin{equation}
\begin{array}{l}{\text { First, calculate the volume of one cell. }} \\ {\qquad V_{c e l l}=\frac{4}{3} r_{c e l l}^{3} \pi=\frac{4}{3}\left(\frac{20}{2} \cdot 10^{-6}\right)^{3} \pi=4.18879 \times 10^{-15} m^{3}} \\ {\text { The volume of the tumor is the volume of } N \text { such cells. Hence, }}\end{array}
\end{equation}
\begin{equation}
\begin{array}{l}{V(t)=V_{c e l l} N(t)} \\ {\Rightarrow \frac{d V}{d t}(t)=\frac{d N}{d t}(t) \cdot V_{c e l l}=\frac{\ln 2}{20} N(t) \cdot V_{c e l l}} \\ {\Rightarrow \frac{d V}{d t}=\frac{\ln 2}{20} V(t)}\end{array}
\end{equation}
