waecmaths question:
A sector of a circle of radius 14cm containing an angle of 60o is folded to form a cone. Calculate the radius of the base of the cone
Option A:
$5\tfrac{1}{2}cm$
Option B:
$4\tfrac{2}{3}cm$
Option C:
$3\tfrac{1}{2}cm$
Option D:
$2\tfrac{1}{3}cm$
waecmaths solution:
\[\begin{align} & \text{The length of the sector }\frac{\theta }{{{360}^{\circ }}}\times 2\pi l=2\pi r \\ & \frac{\theta }{{{360}^{{}^\circ }}}\times 2\pi l=2\pi r \\ & \text{Where }l\text{ is the radius of the sector and }r\text{ is the radius of the cone} \\ & \frac{{{60}^{{}^\circ }}}{{{360}^{{}^\circ }}}\times 2\pi (14)=2\pi r \\ & r=\frac{{{60}^{{}^\circ }}}{{{360}^{{}^\circ }}}\times 14 \\ & r=\frac{7}{3}=2\tfrac{1}{3}cm \\\end{align}\]
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