Let $v$ be the sum of the areas of the regions belonging exclusively to the three small disks in the figure (in light gray) and let $w$ be the area of the region inside belonging exclusively to the largest disk (in dark gray). The diameters of the circles are 6, 4, 4, and 2. Which of the given equalities is true?
(a) $3 v=\pi w$
(c) $v=w$
(e) $\pi v=w$
(b) $3 v=2 w$
(d) $\pi v=3 w$

![](https://cdn.mathpix.com/cropped/2024_05_01_30c9a294a58a6e4b8190g-011.jpg?height=431&width=400&top_left_y=704&top_left_x=1482)
The correct option is (c).

The radii of the three smaller discs are 1, 2, and 2, and the radius of the larger disc is 3. Let's denote by $b$ the blank area. Then

$$
v=1 \pi+4 \pi+4 \pi=9 \pi-b
$$

and $w=9 \pi-b$, that is, $v=w$.

## $A$ area of

保留了源文本的换行和格式，直接输出了翻译结果。