GK 2018 Q18

Let the dimensions of the box be \(x\) cm by \(y\) cm by \(z\) cm as indicated. From the diagram, we have \(2x + 2y = 26\), \(x + z = 10\) and \(y + z = 7\). When we add the last two of these, we obtain \(x + y + 2z = 17\) and, when we then double this, we obtain \(2x + 2y + 4z = 34\). Therefore \(4z = 34 - 26 = 8\) and hence \(z = 2\). Therefore \(x = 8\) and \(y = 5\) and hence the volume of the box in cm³ is 8 × 5 × 2 = 80.