waecmaths question:
The length of the minor and major arcs of a circle are 54cm and 126cm respectively. Calculate the angle of the major sector
Option A:
306o
Option B:
252o
Option C:
246o
Option D:
234o
waecmaths solution:
$\begin{align} & \text{Total length of the arc} \\ & 2\pi r=(126+54)cm=180cm \\ & 2\pi r=180cm \\ & r=\frac{90}{\pi }cm \\ & Length\text{ of the major arc}=\frac{\theta }{{{360}^{\circ }}}\times 2\pi r=126cm \\ & 126=\frac{\theta }{{{360}^{\circ }}}\times 2\times \pi \times \frac{90}{\pi } \\ & \theta ={{126}^{\circ }}\times 2={{252}^{\circ }} \\\end{align}$
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