Let the radius of the base of both the hemisphere and the cone be \(r\) units. And the height of both is equal to the radius of the hemisphere, i.e., \(r\) units. \(\therefore\) Slant height of the cone \(= \sqrt{r^2 + r^2} = \sqrt{2}r\) units. \(\therefore\) Ratio of volumes of the hemisphere and the cone: \(= \frac{2}{3}\pi r^3 : \frac{1}{3}\pi r^2 \cdot r\) \(= \frac{2}{3}\pi r^3 : \frac{1}{3}\pi r^3\) \(= 2 : 1\) And the ratio of curved surface areas of the hemisphere and the cone: \(= 2\pi r^2 : \pi r \cdot \sqrt{2}r\) \(= 2 : \sqrt{2} = \sqrt{2} : 1\) \(\therefore\) The ratio of volumes is \(2 : 1\) and the ratio of curved surface areas is \(\sqrt{2} : 1\).