Formula of the lateral area of a cone:
[tex]LA=\pi *r*s[/tex]s is the slant height
r is the radius
Solve s in the formula above:
[tex]s=\frac{LA}{\pi *r}[/tex]Use the given data to find the slant height:
[tex]\begin{gathered} s=\frac{612\pi cm^2}{\pi *14.2cm} \\ \\ s=\frac{612cm^2}{14.2cm} \\ \\ s=43.1cm \end{gathered}[/tex]Then, the slant height of the given cone is 43.1 centimetersAnswer: C