The area of a sector of a circle with a central angle of $\frac{\pi}{4}$ radians is $11 \mathrm{~cm}^{2}$. Find the radius of the circle. Do not round any intermediate computations. Round your answer to the nearest tenth. \[ \mathrm{cm} \]

Step 1 ：The area of a sector of a circle is given by the formula \(\frac{1}{2}r^{2}\theta\), where \(r\) is the radius of the circle and \(\theta\) is the central angle in radians.

Step 2 ：We know that the area of the sector is \(11 \mathrm{~cm}^{2}\) and the central angle is \(\frac{\pi}{4}\) radians.

Step 3 ：We can use these values to solve for the radius \(r\) of the circle.

Step 4 ：Substituting the given values into the formula, we get \(11 = \frac{1}{2}r^{2} \times 0.7853981633974483\).

Step 5 ：Solving this equation for \(r\), we find that \(r = 5.3\).

Step 6 ：Final Answer: The radius of the circle is \(\boxed{5.3}\) cm.