Let the height of the cone be \(h\), slant height be \(l\), and radius be \(r\) units. \(\therefore \pi rl = \sqrt{10} \times \pi r^2\) i.e., \(l = \sqrt{10}r\) Again, \(h = \sqrt{l^2 - r^2}\) \(= \sqrt{(\sqrt{10}r)^2 - r^2}\) \(= \sqrt{10r^2 - r^2}\) \(= \sqrt{9r^2} = 3r\) \(\therefore h : 2r = 3r : 2r = 3 : 2\)