To find the slant height of a cone with lateral area of [tex]574 \pi \, cm^2[/tex] and a radius of 29 cm, we recall that the lateral area of a cone is given by
[tex]A_L=\pi rl[/tex]
where l is the slant height of the cone.
Thus, [tex]l= \frac{A_L}{\pi r} = \frac{574\pi}{29\pi} \approx 19.79 \, cm[/tex]
