2. Given the vertex of a cone is $P$, the radius of the base is 2, and the height is 1. Take a point $Q$ on the base of the cone such that the angle between the line $P Q$ and the base is no more than $45^{\circ}$. Then the area of the region formed by the points $Q$ that satisfy the condition is . $\qquad$
Answer: $3 \pi$.
Solution: The projection of the cone's vertex $P$ on the base is the center of the base, denoted as $O$. According to the given condition, $\frac{O P}{O Q}=\tan \angle O Q P \leq 1$, which means $O Q \geq 1$. Therefore, the area of the required region is $\pi \cdot 2^{2}-\pi \cdot 1^{2}=3 \pi$.