In the diagram, $A B C D$ is a rectangle, and three circles are positioned as shown. The area of the shaded region, rounded to the nearest $\mathrm{cm}^{2}$, is
(A) 41
(B) 43
(C) 47

![](https://cdn.mathpix.com/cropped/2024_04_20_6027bc27089ed4fc493cg-085.jpg?height=209&width=415&top_left_y=389&top_left_x=1343)
Since three circles touch each other and touch the vertical and horizontal sides of the rectangle, then the width of the rectangle is three times the diameter of the circle, and the height of the rectangle is equal to the diameter of the circle.

![](https://cdn.mathpix.com/cropped/2024_04_20_748fdafcde2a47412608g-376.jpg?height=176&width=376&top_left_y=1050&top_left_x=1384)

Since the width of the rectangle is $24 \mathrm{~cm}$, then the diameter of each circle is $8 \mathrm{~cm}$.

Since the diameter of each circle is $8 \mathrm{~cm}$, then the height of the rectangle is $8 \mathrm{~cm}$, and the radius of each circle is $4 \mathrm{~cm}$.

Therefore, the area of the shaded region is

$$
\begin{aligned}
& \text { Area of shaded region } \\
& =\text { Area of rectangle }- \text { Area of three circles } \\
& =(24 \times 8)-3\left[\pi(4)^{2}\right] \\
& =192-48 \pi \\
& \approx 192-150.80 \quad(\text { using } \pi \approx 3.14) \\
& =41.20
\end{aligned}
$$

Thus, the area of the shaded region is closest to $41 \mathrm{~cm}^{2}$.

ANSwer: (A)