A cylinder and a cone have the same volume and height. If the radius of the cylinder is $5 \mathrm{~cm}$, determine the radius of the cone to the nearest tenth of a centimeter.

Step 1 ：\(V_{cylinder} = V_{cone}\)

Step 2 ：\(\pi r_{cylinder}^2 h = \frac{1}{3} \pi r_{cone}^2 h\)

Step 3 ：\(r_{cylinder}^2 = \frac{1}{3} r_{cone}^2\)

Step 4 ：\(5^2 = \frac{1}{3} r_{cone}^2\)

Step 5 ：\(25 = \frac{1}{3} r_{cone}^2\)

Step 6 ：\(r_{cone}^2 = 75\)

Step 7 ：\(r_{cone} = \sqrt{75}\)

Step 8 ：\(r_{cone} \approx 8.7\)

Step 9 ：\(\boxed{8.7}\)