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 $\text{TRUE?}$
- $R^{2}$ is uniformly distributed in $[0,1]$
- $\pi R^{2}$ is uniformly distributed in $[0,1]$
- $\frac{\pi}{2} R^{2}$ is uniformly distributed in $[0,1]$
- $2 \pi R^{2}$ is uniformly distributed in $[0,1]$
- None of the above