2) Claudia has drawn the initial of her name, a C, on her notebook. The drawing was made by cutting exactly in half a circular ring with an inner radius of $1 \mathrm{~cm}$ and an outer radius of $4 \mathrm{~cm}$. What is the perimeter of the C?
(A) $5 \mathrm{~cm}$,
(B) $5 \pi \mathrm{~cm}$,
(C) $(6+5 \pi) \mathrm{~cm}$,
(D) $(5+6 \pi) \mathrm{~cm}$
(E) $(6+10 \pi) \mathrm{~cm}$
2. The answer is $(\mathbf{C})$.

We can divide the perimeter of the drawing into four parts: two segments $(A B$ and $C D$ ) and two semicircles (arcs $B C$ and $D A$ with radii of $4 \mathrm{~cm}$ and $1 \mathrm{~cm}$, respectively). The length of the segments is equal to the difference between the radii of the two circles: $\overline{A B}=\overline{C D}=3 \mathrm{~cm}$.

The length of the semicircles is half the length of the corresponding circumference: $\overline{B C}=\frac{2 \pi \cdot 4}{2}=4 \pi \mathrm{cm} ; \overline{D A}=\frac{2 \pi \cdot 1}{2}=\pi \mathrm{cm}$. Ultimately, $\overline{A B}+\overline{B C}+\overline{C D}+\overline{D A}^{2}=(6+5 \pi) \mathrm{cm}$.

![](https://cdn.mathpix.com/cropped/2024_04_17_4701f996ee50400fb9c5g-1.jpg?height=396&width=257&top_left_y=1955&top_left_x=1662)