Discussion
The edges of a rectangular box are in the ratio 1 : 2 : 3 and its surface area is 88 cm\(^{2}\). The volume of the box is?
Answer: B
The volume is 48 cm3.
Let the edges be \(x\), \(2x\) and \(3x\). The surface area is twice the sum of the three face areas:
\[ \begin{aligned} 2(2x^{2} + 6x^{2} + 3x^{2}) &= 22x^{2} = 88 \\ x^{2} = 4 &\Rightarrow x = 2 \end{aligned} \]
The edges are 2, 4 and 6 cm, so the volume is \(2 \times 4 \times 6 = 48\) cm3. 24 cm3 is half of it, as if the surface area had been taken without the factor 2.
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