24cm
1) We can find out the slant height of that cone by making use of the following:
[tex]\begin{gathered} R=3 \\ A=\pi r\mleft(s+r\mright) \\ \end{gathered}[/tex]2) Plugging into that we can write out:
[tex]\begin{gathered} 81\pi=3\pi(s+3) \\ \frac{81\pi}{3\pi}=\frac{3\pi(s+3)}{3\pi} \\ 27=s+3 \\ 27-3=s \\ s=24 \end{gathered}[/tex]Hence, the slant height is 24 cm
