$V = 10,000 ~ \tetx{gal.} \times \dfrac{231 ~ \text{in.}^3}{1 ~ \text{gal.}} \times \left( \dfrac{1 ~ \text{ft.}}{12 ~ \text{in.}} \right)^3$
$V = 1336.806 ~ \text{ft.}^3$
$V_{cylinder} + V_{cone} = V$
$\pi r^2 h_1 + \frac{1}{3}\pi r^2 h_2 = V$
$\pi r^2(3r) + \frac{1}{3}\pi r^2(2r) = 1336.806$
$\frac{11}{3}\pi r^3 = 1336.806$
$r = 4.878 \, \text{ft.}$
$h_1 = 3(4.878) = 14.634 ~ \text{ft.}$
$h_2 = 2(4.878) = 9.756 ~ \text{ft.}$
$A = A_{L-cylinder} + A_{L-cone}$
$A = 2\pi rh_1 + \pi rL$
$A = 2\pi(4.878)(14.634) + \pi(4.878)\sqrt{4.878^2 + 9.756^2}$
$A = 615.68 ~ \text{ft.}^2$ answer