An arc of a circle of radius 6cm is 8cm long. Find the area of the sector

A.

5\(\frac{1}{3}\)cm2

B.

24cm2

C.

36cm2

D.

84cm2

Correct answer is B

Radius of the circle r = 6cm, Length of the arc = 8cm

Area of sector = \(\frac{\theta}{360}\) x \(\pi\)r2........(i)

Length of arc = \(\frac{\theta}{360}\) x 2\(\pi\)r........(ii)

from eqn. (ii) \(\theta\) = \(\frac{240}{\pi}\), subt. for \(\theta\) in eqn (i)

Area x \(\frac{240}{1}\) x \(\frac{1}{360}\) x \(\frac{\pi 6}{1}\)

= 24cm\(^2\)