To find the slant height (l) of a cone, we can use the Pythagorean theorem. The slant height forms a right triangle with the height (h) and the radius (r) of the base of the cone.
Given:
- Height (h) of the cone = 8 ft
- Radius (r) of the base = 15 ft
The formula to find the slant height is:
\[ l = \sqrt{r^2 + h^2} \]
Substituting the values:
\[ l = \sqrt{15^2 + 8^2} \] \[ l = \sqrt{225 + 64} \] \[ l = \sqrt{289} \] \[ l = 17 \text{ ft} \]
Therefore, the slant height of the cone is 17 feet.