The area of a circle with radius $r$ is calculated using the formula $A = \pi r^{2}$. A car has a wiper on its semicircular rear window that can rotate around point O. This wiper cleans points on the window that are at least 1 unit and at most 5 units away from point O. When this wiper is operated and rotates $120^{\circ}$ as shown in the figure, the area cleaned by the wiper is half the area of the window. Accordingly, what is the radius of the window in units? A) $4\sqrt{2}$ B) $5\sqrt{2}$ C) $6\sqrt{2}$ D) $4\sqrt{3}$ E) $5\sqrt{3}$
The area of a circle with radius $r$ is calculated using the formula $A = \pi r^{2}$.
A car has a wiper on its semicircular rear window that can rotate around point O. This wiper cleans points on the window that are at least 1 unit and at most 5 units away from point O. When this wiper is operated and rotates $120^{\circ}$ as shown in the figure, the area cleaned by the wiper is half the area of the window.
Accordingly, what is the radius of the window in units?
A) $4\sqrt{2}$\\
B) $5\sqrt{2}$\\
C) $6\sqrt{2}$\\
D) $4\sqrt{3}$\\
E) $5\sqrt{3}$