waecmaths question:
A chord subtends an angle of 120o at the centre of a circle of radius 3.5cm. Find the perimeter of the minor sector containing the chord[Take $\pi =\tfrac{22}{7}$]
Option A:
$14\tfrac{1}{3}cm$
Option B:
$12\tfrac{5}{6}cm$
Option C:
$8\tfrac{1}{7}cm$
Option D:
$7\tfrac{1}{3}cm$
waecmaths solution:
$\begin{align} & Perimeter=\frac{\theta }{{{360}^{\circ }}}\times 2\pi r+2r \\ & Perimeter=\frac{{{120}^{\circ }}}{{{360}^{\circ }}}\times 2\times \frac{22}{7}\times 3.5+2(3.5) \\ & Perimeter=\frac{1}{3}\times 22+7=\frac{22}{3}+7=\frac{22+21}{3}=\frac{43}{3} \\ & Perimeter=14\frac{1}{3}cm \\\end{align}$
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