1. Let's state the problem: We want to find a simpler formula to calculate the height of a small cone. 2. Assume the small cone is similar to a larger cone, meaning their corresponding dimensions are proportional. 3. Let the height of the large cone be $H$, the height of the small cone be $h$, the radius of the large cone be $R$, and the radius of the small cone be $r$. 4. Since the cones are similar, the ratio of their heights equals the ratio of their radii: $$\frac{h}{H} = \frac{r}{R}$$ 5. Solving for $h$, the height of the small cone, we get: $$h = H \times \frac{r}{R}$$ 6. This formula allows you to find the height of the small cone directly if you know the height and radius of the large cone and the radius of the small cone. Final answer: $$h = H \times \frac{r}{R}$$