WAEC Mathematics 2014 Paper

Concept:The sector area becomes the curved surface area of the cone, and the radius of the original circle becomes the slant height of the cone.Explanation:The diameter of the circle is $12$ cm, so its radius is $\frac{12}{2} = 6$ cm.This radius becomes the slant height $l = 6$ cm of the cone formed by folding the sector.The area of the sector is given as $66\, \text{cm}^2$, which equals the curved surface area of the cone.Curved surface area of a cone is $\pi r l$, where $r$ is the radius of the cone's base.Thus, $66 = \pi \times r \times 6$.Substitute $\pi = \frac{22}{7}$: $66 = \frac{22}{7} \times r \times 6$.Simplify: $66 = \frac{132}{7} r$.Divide both sides by $6$: $11 = \frac{22}{7} r$.Multiply through by $7$: $77 = 22r$.So, $r = \frac{77}{22} = 3.5$ cm.Answer:$3.5$ cm, which is Option B.