Question 16

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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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