How to solve this
The ratio of curved surface area of a cylinder and cone is 8:5. What will be the ratio of their heights if the radius and height of cylinder is same. Cone is placed on cylinder.

The radius of the cylinder and its height is same. Thus, its curved surface area is $$2\pi rh=2\pi r^{2}$$. Since the cone is placed on the cylinder, its radius must be equal to that of the cylinder. Its curved surface area becomes $$2\pi rl$$. Now the ratio of area is 8:5, this means :
$$\frac{2\pi r^{2}}{\pi rl}=\frac{8}{5}=>\frac{r}{l}=\frac{4}{5}$$. We need to find the ratio of height of cylinder to height of cone. Lets suppose height of the cone is h. We want the ratio r/h since height of cylinder is equal to r.
$$\frac{r}{l}=\frac{r}{\sqrt{{r^{2}+h^{2}}}}=\sqrt{\frac{r^{2}}{r^{2}+h^{2}}}$$. Let r/h be x. Dividing numerator and denominator by $$h^{2}$$, we get:
$$\sqrt{\frac{x^{2}}{x^{2}+1}}=\frac{4}{5}=>\frac{x^{2}}{x^{2}+1}=\frac{16}{25}=>x^{2}=\frac{16}{9}=>x=\frac{4}{3}$$.