Let \(S\) be the sphere of radius \(R\) centered at the origin. Explain using symmetry:

\[
\iint_{S} x^{2} d S=\iint_{S} y^{2} d S=\iint_{S} z^{2} d S
\]

Then show that \(\iint_{S} x^{2} d S=\frac{4}{3} \pi R^{4}\) by adding the integrals.