Question 17

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waecmaths question: 

A sector of a circle which subtends 172o at the centre of the circle has a perimeter of 600cm. Find, correct to the nearest cm, the radius of the circle [Take $\pi =\tfrac{22}{7}$]

Option A: 

120cm

Option B: 

116cm

Option C: 

107cm

Option D: 

100cm

waecmaths solution: 

$\begin{align}  & Perimeter=\left( \frac{\theta }{360}\times 2\pi r+2r \right) \\ & 600=\frac{{{172}^{\circ }}}{{{360}^{\circ }}}\times 2\times \frac{22}{7}\times r+2r \\ & 600=3.003174603r+2r \\ & 5.003174603r=600 \\ & r=\frac{600}{5.003174603} \\ & r=119.9238578 \\ & \text{To nearest cm }r=120cm \\\end{align}$

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