Answer
a) $222.612$
b) $93.914$
Work Step by Step
Given \begin{equation}
L(M)=0.0165 \sqrt[3]{M}.
\end{equation} First solve for $M$ in term of $L$.
\begin{equation}
\begin{aligned}
0.0165 \sqrt[3]{M}&=L\\
\sqrt[3]{M}&=\frac{L}{0.0165 } \\
\left(\sqrt[3]{M}\right)^3& =\left( \frac{L}{0.0165 } \right)^3\\
M& = \left( \frac{L}{0.0165 } \right)^3.
\end{aligned}
\end{equation} a) Now, set $L= 0.1$ to find the live body mass of the museum specimen.
\begin{equation}
\begin{aligned}
M& = \left( \frac{0.1}{0.0165 } \right)^3\\
&=222.612.
\end{aligned}
\end{equation} The live body mass of the museum specimen is about $222.612$.
b) Set $L= 0.075$ to find the live body mass of the museum specimen.
\begin{equation}
\begin{aligned}
M& = \left( \frac{0.075}{0.0165 } \right)^3\\
&=93.914.
\end{aligned}
\end{equation} The live body mass of the museum specimen is about $93.914$.
