# How to solve Power Density Function?

How to solve this problem:

A radio receiver needs $$1 \textrm{ nW/}\textrm{m}^2$$ of power density function, how far away from a 1-watt point source will it continue to work?

Then $$\frac{P}{A} = S = 1*10^{-9} = \frac{1}{4 \pi r^2}$$ Then $$r = \frac{500}{\sqrt{\pi}} ~= 159m$$
So at a maximum distance of 159 meters your radio receiver can still operate. Note that this is an upper bound obiously. So for any distance $$r \leq 159 m$$ your radio receiver will work.