WAEC Mathematics 2013 Paper

Concept:The volume of a cone is found using the base radius and the perpendicular height, not the slant height.Explanation:The formula for the volume of a cone is $V = \frac{1}{3}\pi r^2 h$.Here, slant height $l = 5\text{ cm}$ and radius $r = 3\text{ cm}$.Use Pythagoras' theorem to find the perpendicular height $h$: $l^2 = r^2 + h^2$.So, $h^2 = 5^2 - 3^2 = 25 - 9 = 16$.Thus, $h = \sqrt{16} = 4\text{ cm}$.Now substitute into the volume formula: $V = \frac{1}{3} \times \frac{22}{7} \times 3^2 \times 4$.Simplify: $V = \frac{1}{3} \times \frac{22}{7} \times 9 \times 4 = \frac{22 \times 3 \times 4}{7} = \frac{264}{7}$.Therefore, $V = 37.71\text{ cm}^3$.Correct to the nearest whole number, the volume is $38\text{ cm}^3$.Answer:C. $38\text{ cm}^3$