#### Answer

The solution is $r=9.8696$.

#### Work Step by Step

We need to solve the inequality $| r - \pi^{2} | < 10^{-4} $.
That is what we have
$ -10^{-4} \lt r - \pi^{2} \lt 10^{-4} $
$ -10^{-4} + \pi^{2}\lt r \lt 10^{-4} + \pi^{2} $
We know that $\pi$ is not a rational number and neither is $\pi^2$. So, we can not have the solution $r = \pi^2$ be between $-10^{-4} + \pi^{2}$ and $10^{-4} + \pi^{2}$.
A close estimation of a rational number to the irrational number $\pi^2$, we can choose $r=9.8696$. Thus, the solution is $r=9.8696$.