The angle of a sector of a circle radius 10.5 cm is 48\(^o\). Calculate the perimeter of the sector.

A.

25.4cm

B.

25.4cm

C.

25.6cm

D.

29.8cm

Correct answer is D

The lenght of Arc AB = \(\frac{Q}{360}\) 2\(\pi\)r

= \(\frac{48}{360}\) x 2\(\frac{22}{7}\) x 10.5 = \(\frac{48}{360}\) x 2\(\frac{22}{7}\) x \(\frac{21}{2}\)

= \(\frac{4 \times 22 \times 3}{30} \times \frac{88}{10}\) = 8.8cm 

Perimeter = 8.8 + 2r = 8.8 + 2r 

= 8.8 + 2(10.5)

= 8.8 + 21

= 29.8cm