Look at the cone below.

15 ft15\ \text{ft}15 ft

lll

8 ft8\ \text{ft}8 ft

How many feet long is the slant height of the cone? Click Here for Help Video.

1 answer

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.