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
7\(\frac{2}{10}\) cm
C
6 \(\frac{4}{5}\) cm
D
13 \(\frac{3}{5}\) cm
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
Angle of sector = 108^\circ;
Radius of circle = 3\(\frac{1}{2}\)cm ⇒ \(\frac{7}{2}\) cm
Perimeter of sector = 108/360 \times 2\pir + 2r ⇒ \(\frac{108}{360 }\) \times 2 \times \(\frac{22}{7}\) \times \(\frac{7}{2}\) + 2(\(\frac{7}{2}\)) ⇒ 66/10 + 7 cm = 6\(\frac{3}{5}\) + 7 = 13\(\frac{3}{5}\)
Source: Myschool Past Questions Archive (Record #75855)