208. Given: height $h$ and radii $r$ and $R$ of the upper and lower bases of a frustum of a cone, find the height of the corresponding complete cone.
208. By completing the given truncated cone (Fig. 52), we have $x: r = x+h: R$, from which $x = \frac{r h}{R-r}$, therefore, $x+h = \frac{R h}{R-r}$. This expression was known even to Al-Karaji.

![](https://cdn.mathpix.com/cropped/2024_05_21_926f0bb262c8f9569516g-126.jpg?height=417&width=386&top_left_y=1616&top_left_x=1318)

Fig. 52.