WAEC Mathematics 2019 Paper

Concept:Total surface area of a cylinder is the sum of the curved surface area and the two circular ends.For radius $r$ and height $h$, it is given by $2\pi rh + 2\pi r^2$.Explanation:The total surface area is $165 \, \text{cm}^2$.The base diameter is $7 \, \text{cm}$, so the radius is$$r = \frac{7}{2} \, \text{cm}.$$Using $\pi = \frac{22}{7}$, substitute into the formula:$$165 = 2 \times \frac{22}{7} \times \frac{7}{2} \times h + 2 \times \frac{22}{7} \times \frac{7}{2} \times \frac{7}{2}.$$The first term simplifies to $22h$ and the second term simplifies to $77$.So, $$165 = 22h + 77.$$Subtract $77$ from both sides:$$88 = 22h.$$Divide both sides by $22$:$$h = \frac{88}{22} = 4.$$Therefore, the height of the cylinder is $4.0 \, \text{cm}$.Answer:C. $4.0 \, \text{cm}$