A piece of wire is in the form of a sector of a circle of radius 20 cm subtending an angle 150o at t...........

Quantitative Aptitude (CDS) Mensuration 2D

A piece of wire is in the form of a sector of a circle of radius 20 cm, subtending an angle 150^o at the centre . If it is bent in the form of circle, then what will be its radius?

$\frac{19}{3}\: cm$

7 cm

8 cm

None of the above.

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Explanation:

$150^{o}=\frac{5}{6}\pi$
$length\: of \: the\: arc\: = \frac{5}{6}\pi \times20$
this length of the arc+ 40 = perimeter of new circle = 2 $\pi$ r
$\frac{5}{6}\pi \times20+ 40 = 2 \pi r$
$=> \frac{50}{3}\pi + 40 = 2 \pi r$
$=> \frac{25}{3}+ \frac{20}{\pi } = r$
$=> \frac{25}{3}+ \frac{70}{11} = r$
$=> r=\frac{485}{11}$