17. The areas of the three faces of a cuboid that meet at a vertex are $6 \mathrm{~cm}^{2}, 10 \mathrm{~cm}^{2}, 15 \mathrm{~cm}^{2}$, respectively. Then the surface area $S$ of the circumscribed sphere of this cuboid is $\qquad$.
17. Let the length, width, and height of the rectangular prism be $x, y, z$, respectively, then $\left\{\begin{array}{l}x y=6 \\ y z=10 \\ z x=15\end{array} \Rightarrow\left\{\begin{array}{l}x=3, \\ y=2, \\ z=5 .\end{array}\right.\right.$ Therefore, the length of the diagonal $l=\sqrt{2^{2}+3^{2}+5^{2}}=\sqrt{38}, \therefore \quad S=\pi l^{2}=38 \pi$.