waecmaths question:
The area of a sector of a circle with diameter 12cm is 66cm2. If the sector is folder to form a cone, calculate the radius of the base of the cone. [Take $\pi =\tfrac{22}{7}$]
Option A:
3.0cm
Option B:
3.5cm
Option C:
7.0cm
Option D:
7.5cm
waecmaths solution:
$\begin{align} & \text{Consider these sector} \\ & \frac{\theta }{{{360}^{\circ }}}\times 2\pi l=2\pi r \\ & \frac{\theta }{{{360}^{\circ }}}=\frac{r}{l}----(i) \\ & \text{Area of the sector} \\ & \frac{\theta }{{{360}^{\circ }}}\times \pi {{l}^{2}}=66 \\ & \text{Substitute }\frac{r}{l}=\frac{\theta }{{{360}^{\circ }}} \\ & \frac{r}{l}\times \pi {{l}^{2}}=66 \\ & \frac{r}{6}\times \frac{22}{7}\times 36=66 \\ & r=3.5 \\\end{align}$
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