WAEC Mathematics 2025 Paper

Concept:For a sphere, equate its volume and surface area expressions to find the radius, then double it to get the diameter.Explanation:Volume of a sphere is $V = \frac{4}{3}\pi r^3$.Surface area of a sphere is $A = 4\pi r^2$.Since both numerical values equal $k$, we equate them:$$\frac{4}{3}\pi r^3 = 4\pi r^2$$Cancel $4\pi$ from both sides:$$\frac{1}{3}r^3 = r^2$$Multiply through by $3$:$$r^3 = 3r^2$$$$r^3 - 3r^2 = 0$$$$r^2(r - 3) = 0$$The non-zero solution is $r = 3$ cm.Therefore, the diameter is $$d = 2r = 2 \times 3 = 6 \text{ cm}$$Answer:The diameter of the sphere is $6$ cm, so the correct option is D.