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

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

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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 $^2$

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