Pile of sand

The volume is given by the formula: $V=\dfrac{1}{3} \pi r^2 h$ .

Substituting, we get

$\dfrac{1}{3} \pi r^2 (8)=\dfrac{128 \pi}{3}$ $\implies$ $r^2(8)=128$ $\implies$ $r^2=16$ $\implies$ $r=\sqrt{16}=4$

By pythagorean theorem , the slant height is

$L=\sqrt{8^2+4^2}=\sqrt{64+16}=\sqrt{80}=4\sqrt{5}$

The lateral area of a cone is given by the formula: $A=\dfrac{1}{2}cL$ where $c$ = circumference of the base and $L$ = slant height.

Substituting, we get

$A=\dfrac{1}{2}(2)(\pi)(4)(4\sqrt{5})$

$A=$ $\boxed{16\sqrt{5} \pi}$