Answer
$$r = \sqrt[3] {16000}= 25.20$$
Work Step by Step
Let us call the amount of wood $W$, the heat $q$ and the distance to the fire $r$.
The equation that models this is
$$q = W/ r^3$$
Plugging in $ r = 20$ and $W = x$
$$q=x/8000$$
Realizing that $x$ is being doubled,
$$q = 2x/r^3 = x/8000$$
$$1/r^3 = 1/16000$$
Solving,
$$r = \sqrt[3] {16000}= 25.20$$
