I4.2 In Figure 1, the shaded area is formed by two concentric circles and has area $96 \pi \mathrm{cm}^{2}$. If the two radii differ by $2 P \mathrm{~cm}$ and the large circle has area $Q \mathrm{~cm}^{2}$, find the value of $Q$. (Take $\pi=3$ )

I4.3 Let $R$ be the largest integer such that $R^{Q}<5^{200}$, find the value of $R$.
Let the radii of the large and small circles be $R$ and $r$ respectively.
$$
\begin{array}{l}
\pi\left(R^{2}-r^{2}\right)=96 \pi \text { and } R-r=8 \ldots \text { (1) } \\
(R+r)(R-r)=96 \Rightarrow(R+r) \times 8=96 \Rightarrow R+r=12 \ldots \\
(2)+(1): 2 R=20 \Rightarrow R=10 \Rightarrow Q=\pi(10)^{2}=300
\end{array}
$$
$R^{300}<5^{200} \Rightarrow R^{3}<25$, the largest integer is 2 .