WAEC Mathematics 2024 Paper

Concept: Use the equal volume condition of a cone and a cylinder to relate their heights.Explanation:Let the radius of the cylinder be $r$.Then the base radius of the cone is $2r$.Let the height of the cylinder be $H$ and the height of the cone be $h$.Volume of the cylinder $= \pi r^{2}H$.Volume of the cone $= \frac{1}{3}\pi (2r)^{2}h = \frac{1}{3}\pi \cdot 4r^{2}h = \frac{4}{3}\pi r^{2}h$.Since volumes are equal, $\pi r^{2}H = \frac{4}{3}\pi r^{2}h$.Cancel $\pi r^{2}$ from both sides: $H = \frac{4}{3}h$.Therefore, $\frac{H}{h} = \frac{4}{3}$, which gives the ratio $H : h = 4 : 3$.Answer: B. $4 : 3$