Let the radius of the large semicircle be \(R\).<br><br>The diameter of the small semicircle = \(R\), so its radius = \(\frac{R}{2}\).<br><br>Area of small semicircle = \(\frac{1}{2}\pi(\frac{R}{2})^2 = \frac{\pi R^2}{8}\).<br>Area of large semicircle = \(\frac{1}{2}\pi R^2 = \frac{\pi R^2}{2}\).<br><br>Ratio = \(\frac{\pi R^2}{8} : \frac{\pi R^2}{2} = \frac{1}{8} : \frac{1}{2} = 1 : 4\).<br><br>Final Answer: C: 1 : 4