Step 1 :The diameter of the sphere is given as 21 cm.
Step 2 :Since the radius is half of the diameter, the radius of the sphere is \(\frac{21}{2} = 10.5\) cm.
Step 3 :The formula for the surface area of a sphere is \(4\pi r^2\), where \(r\) is the radius of the sphere.
Step 4 :Substituting the radius into the formula, we get \(4\pi (10.5)^2\).
Step 5 :Calculating the above expression, we find that the surface area of the sphere is approximately 1385 square centimetres.
Step 6 :\(\boxed{1385}\) square centimetres is the surface area of the sphere, to the nearest square centimetre.