Verified Answer :

\(A=\frac12\pi w^2*2Lw\\\\A=\frac12*2\pi w^2*w*L\\\\ A=\pi w^3L\)
If we divide both sides by πw³ we'll got the L:
                                                                         \(A:(\pi w^3)=\pi w^3L:(\pi w^3)\\\\ \dfrac A{\pi w^3}=L\\\\ L=\dfrac A{\pi w^3}\)