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Consider a unit disc $D$. Let a point $x$ be chosen uniformly on $D$ and let the random distance to $x$ from the center of $D$ be $R$. Which of the following is $\text{TRUE?}$

  1. $R^{2}$ is uniformly distributed in $[0,1]$
  2. $\pi R^{2}$ is uniformly distributed in $[0,1]$
  3. $\frac{\pi}{2} R^{2}$ is uniformly distributed in $[0,1]$
  4. $2 \pi R^{2}$ is uniformly distributed in $[0,1]$
  5. None of the above
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