WAEC Mathematics 2025 Paper

Concept:The original cone and the smaller cone cut off at the top are similar, so their radii and heights are proportional.Explanation:Let $O$ be the vertex of the complete cone.Let $x = OA$, the height of the small cone that is cut off.The frustum has height $12\text{ cm}$, so the total height of the cone is $OB = x + 12$.From the diagram, the radius of the small cone is $AD = 6\text{ cm}$ and the radius of the large cone is $BC = 12\text{ cm}$.Since triangles $OAD$ and $OBC$ are similar:$$\frac{OA}{OB} = \frac{AD}{BC}$$Substituting the values:$$\frac{x}{x+12} = \frac{6}{12}$$Simplifying:$$\frac{x}{x+12} = \frac{1}{2}$$Cross-multiply:$$2x = x+12$$$$x = 12$$Therefore, the height of the cone is:$$OB = x+12 = 12+12 = 24\text{ cm}$$Answer:$24\text{ cm}$ — Option A.