Step 1 :Given that the diameter of Sphere H is 9 cm, we can calculate the radius as half of the diameter. So, the radius is \(\frac{9}{2} = 4.5\) cm.
Step 2 :The formula for the surface area of a sphere is \(4\pi r^2\). Substituting the value of the radius into the formula, we get \(4\pi (4.5)^2\).
Step 3 :Calculating the above expression, we find that the surface area of Sphere H is approximately 254.47 cm^2.
Step 4 :So, the final answer is \(\boxed{254.47 \, \text{cm}^2}\).