sandy wrote:
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If O is the center of the circle, what is the perimeter of the sector with central angle 72°?
(A) \(5 + 2\pi\)
(B) \(10 + 2\pi\)
(C) \(10 + 4\pi\)
(D) \(10 + 5\pi\)
(E) \(20 + 2\pi\)
Name the points as A and B where radius touch the circumference of the circle O.
Perimeter of minor Sector AOB = radius + radius + minor Arc length AB
We know radius (r) = 5
minor Arc length AB = \(\frac{72}{360}\) x \(2πr\) = \(\frac{1}{5}\) x \(10π\) = \(2π\)
Therefore, Perimeter of minor Sector AOB = \(5 + 5 + 2π\) = \(10 + 2π\)
Hence, option B