Let \(U\) be uniformly on a disc of radius \(\ell\) centered at the origin. Express in polar coordinates \(U = (R, \theta)\). To compute the distribution of \(R\), observe that
\[ \begin{eqnarray*} \mathbb{P}(R \leq r) &=& \frac{\pi r^2}{\pi \ell^r} \\ &=& (r/\ell)^2 \end{eqnarray*} \]
In particular, we see that \(R\) is not uniformly distributed. Specifically,
\[ \mathbb{P}(R > \ell/2) = 1 - (1/2)^2 = 3/4,\]
so we see that \(3/4\) is the area is accounted for by the region of the disc where the radius exceeds a \(1/2\).