Let the height of the cone be equal to its diameter, i.e., \( h \) units. \(\therefore\) Radius \( = \frac{h}{2} \) units. \(\therefore\) Slant height \( (l) = \sqrt{h^2 + \left(\frac{h}{2}\right)^2} = \sqrt{\frac{5h^2}{4}} = \frac{\sqrt{5}h}{2} \) \(\therefore\) Ratio of curved surface area to base area \( = \pi \times \frac{h}{2} \times \frac{\sqrt{5}h}{2} : \pi \left(\frac{h}{2}\right)^2 = \sqrt{5} : 1 \)