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A right cone is inscribed in a sphere of radius \( R \). Let \( S=f(x) \) be the functional relationship between the lateral surface area \( S \) of the cone and its generatrix \( x \).
- The value of \( f(R) \) is given by
(a) \( \sqrt{3} \pi R^{2} \)
(b) \( \frac{\sqrt{3}}{2} \pi R^{2} \)
(c) \( \pi R^{2} \)
(d) \( 2 \pi R \)
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