In the diagram above, O is the center if the two concentric circle of radii 13cm and 10cm respectively. Find the area of the shaded portion in the sector with angle 120^\circ at the center
Attached Figure / Diagram
A
\(\frac{1}{3}\pi cm^2\)
B
\(\pi cm^2\)
C
\(3\pi cm^2\)
D
\(23\pi cm^2\)
E
\(46\pi cm^2\)
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
\(\frac{120\pi}{360}(R^2 - r^2)\)
= \(\frac{1}{3}\times \pi (13^2 - 10^2)\)
= \(\frac{1}{3}\times \pi \times 69\) = 23\(\pi cm^2\)
Source: Myschool Past Questions Archive (Record #26340)