The angle of a sector of a circle is 108^\circ. If the radius of the circle is 3\(\frac{1}{2}\)cm, find the perimeter of the sector
A
6 \(\frac{3}{5}\)cm
B
6 \(\frac{4}{5}\)cm
C
7 \(\frac{1}{10}\)cm
D
10 \(\frac{2}{5}\)cm
E
13 \(\frac{3}{5}\)cm,
Verified Correct Answer: E.
Step-by-Step Mathematical Solution
Perimeter of sector = \(\frac{\theta}{360^\circ} \times 2\pi r + 2r\)
= \(\frac{108}{360} \times 2 \times \frac{22}{7} \times \frac{7}{2} + 2(\frac{7}{2})\)
= \(6 \frac{3}{5} + 7\)
= \(13 \frac{3}{5} cm\)
Source: Myschool Past Questions Archive (Record #23747)