WAEC Mathematics 2025 Paper

Concept:When a sector is bent to form a cone, the arc length of the sector becomes the circumference of the base of the cone.Explanation:The circumference of the original circle is $2\pi R = 2\pi \times 21 = 42\pi$ cm.The sector angle is $120^\circ$, which is $\frac{120}{360} = \frac{1}{3}$ of the full circle.So, the arc length of the sector is $\frac{1}{3} \times 42\pi = 14\pi$ cm.This arc length is equal to the circumference of the cone's base.Therefore, $2\pi r = 14\pi$.Dividing both sides by $2\pi$, we get $r = 7$ cm.This matches the direct formula: $r = \frac{\theta}{360}R = \frac{120}{360} \times 21 = 7$ cm.Answer:D. 7 cm