JAMB Mathematics 2023 Paper

Concept:The volume of a cone is given by $V = \frac{1}{3}\pi r^{2}h$, where $h$ is the vertical height. Since the slant height is given, first find $h$ using Pythagoras' theorem.Explanation:The cone has base radius $r = 5$ cm and slant height $l = 13$ cm.The radius, height, and slant height form a right triangle: $l^{2} = r^{2} + h^{2}$.So, $13^{2} = 5^{2} + h^{2}$.This gives $169 = 25 + h^{2}$.Hence, $h^{2} = 169 - 25 = 144$.Therefore, $h = \sqrt{144} = 12$ cm.Now substitute into the volume formula: $V = \frac{1}{3}\pi (5^{2})(12)$.This simplifies to $V = \frac{1}{3}\pi \times 25 \times 12 = 100\pi$ cm$^{3}$.Answer:D. $100\pi$ cm$^{3}$