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A piece of paper in the shape of a sector of a circle (see Fig. 1) is rolled up to form a right-circular cone (see Fig. 2). The value of the angle $\theta$ is.
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The correct answer is:
$\frac{9 \pi}{13}$
Slant height $=13$
$\begin{array}{l}
\theta=\frac{\mathrm{S}}{\mathrm{r}} \\
\Rightarrow \mathrm{S}=\mathrm{r} \theta \\
\Rightarrow 2 \pi(5)=13 \mathrm{\theta} \\
\Rightarrow \theta=\frac{10 \pi}{13}
\end{array}$
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