WAEC Mathematics 2012 Paper

Concept:Use the volume of a cuboid to find its dimensions from the given ratio, then apply the total surface area formula.Explanation:Let the common ratio factor be $x$.Then length $= 2x$, width $= x$, and height $= x$.Volume $= \text{length} \times \text{width} \times \text{height} = 2x \times x \times x = 2x^3$.Given volume $= 54 \ \mathrm{cm}^3$, so $2x^3 = 54$.Therefore, $x^3 = \frac{54}{2} = 27$, giving $x = \sqrt[3]{27} = 3$.Thus, length $= 2(3) = 6 \ \mathrm{cm}$, width $= 3 \ \mathrm{cm}$, height $= 3 \ \mathrm{cm}$.Total surface area $= 2(lb + lh + bh)$.$= 2[(6 \times 3) + (6 \times 3) + (3 \times 3)]$$= 2[18 + 18 + 9] = 2[45] = 90 \ \mathrm{cm}^2$.Answer:The total surface area is $90 \ \mathrm{cm}^2$, so the correct option is B.