The circumference of a circle with radius r is $\text{C} = 2\pi r$, and the area of a circle with radius r is calculated with the formula $A = \pi r^{2}$. In the figure; a rope that completely wraps around a semicircle with radius R once is unwound and divided into three equal parts. One of these equal parts completely wraps around a semicircle with radius r once. Accordingly, what is the ratio of the area of the semicircle with radius $R$ to the area of the semicircle with radius $\mathbf{r}$? A) 3 B) 4 C) 6 D) 8 E) 9
The circumference of a circle with radius r is $\text{C} = 2\pi r$, and the area of a circle with radius r is calculated with the formula $A = \pi r^{2}$.
In the figure; a rope that completely wraps around a semicircle with radius R once is unwound and divided into three equal parts. One of these equal parts completely wraps around a semicircle with radius r once.
Accordingly, what is the ratio of the area of the semicircle with radius $R$ to the area of the semicircle with radius $\mathbf{r}$?
A) 3
B) 4
C) 6
D) 8
E) 9