Gun Goofed

In this question, we are looking at inverse proportion.

Let $x$ be the number of shots and let $r$ be the radius of the shot.

From the question we have,

$\begin{aligned} n & =\frac { k }{ { r }^{ 3 } } \end{aligned}$ where $k$ is a constant of proportionality.

Substituting $n=4096$ and $r=1$ we have,

$\begin{aligned} 4096 & =\frac { k }{ { 1 }^{ 3 } } \\ \therefore \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, k & =4096 \end{aligned}$

Substituting $k=4096$ we have,

$\begin{aligned} n & =\frac { 4096 }{ { 1.6 }^{ 3 } } \\ & =\frac { 4096 }{ 4.096 } \\ & =\boxed { 1000 } \end{aligned}$