A frustum of a cone has end radii 15 cm and 9 cm and a vertical height of 8 cm. Find the slant height of the COMPLETE cone from which it was cut.

Let the whole cone have height $H$. By similar triangles $\frac{9}{15}=\frac{H-8}{H}$, so $\frac{2}{5}H=8$ and $H=20$ cm, with base radius 15 cm. Its slant height = $\sqrt{20^2+15^2}=\sqrt{625}=25$ cm. 10 cm is the FRUSTUM’s slant height $\sqrt{8^2+6^2}$; 20 cm is the whole cone’s height, not its slant; 17 cm pairs the frustum’s height 8 with the base radius 15.