2. (8 points) In the figure, two sectors with central angles of $90^{\circ}$ are placed on the large circle, and the small circle is placed on the two sectors, with all their centers at the same point. If the radius ratio of the small circle, the large circle, and the sectors is 1: 3: 4, then the shaded area occupies $\qquad$ $\%$ of the entire figure area.
【Solution】Solution: According to the problem, we have:
Let the radii of the three circles be $1, 3, 4$.
The area of the entire figure is: $\frac{1}{2} \pi \times 4 \times 4 + \frac{1}{2} \pi \times 3 \times 3 = 12.5 \pi$. The area of the shaded part is: $\frac{1}{2}(\pi \times 3 \times 3 - \pi \times 1 \times 1) = 4 \pi$. Therefore, the proportion of the shaded part to the entire logo area is $\frac{4 \pi}{12.5 \pi} = 32\%$. Hence, the answer is: 32