Correct Answer: $\frac{27 \sqrt{2}}{8} \mathrm{~cm}$

Solution : Given: The three sides of the triangle are 9 cm, 6 cm, and 5 cm respectively.
Let $a, b$, and $c$ be the sides of the triangle.
We know that,
Area of triangle = $\sqrt{s(s - a) (s - b) (s - c)}$
Where $s = \frac{(a + b + c)}{2} = \frac{20}{2} = 10\ \text{cm}$
Area = $\sqrt{10 × (10 - 9) × (10 - 6) × (10 - 5)}=\sqrt{200}=10\sqrt{2}$
Circumradius = $\frac{\text{Product of the sides}}{4\times \text{Area}}=\frac{9\times6\times5}{4\times \text{Area}}=\frac{270}{40\sqrt{2}}=\frac{27 \sqrt{2}}{8}$
Hence, the correct answer is $\frac{27 \sqrt{2}}{8} \mathrm{~cm}$.