The table shows the dimensions of three cuboid boxes. Box Length Width Height A \(20\) cm \(10\) cm \(8\) cm B \(15\) cm \(12\) cm \(9\) cm C \(18\) cm \(11...

All three parts rest on the cuboid volume formula \(V = l \times w \times h\). Part (b) asks you to show a result, which means the supporting figures must actually be calculated and compared, not just asserted.

1. (a) Box A: \(20 \times 10 \times 8 = 1600\) cm\(^3\) [B1].

1. (b) Box B: \(15 \times 12 \times 9 = 1620\) cm\(^3\), and box C: \(18 \times 11 \times 8 = 1584\) cm\(^3\). Both volumes are needed [M1].
2. Comparing all three, \(1620 > 1600 > 1584\), so box B has the greatest volume [A1].

1. (c) The three boxes together occupy \(1600 + 1620 + 1584 = 4804\) cm\(^3\), so the empty space is \[ 8000 - (1600 + 1620 + 1584) \] [M1]
2. The volume of empty space is \(3196\) cm\(^3\) [A1].

Box B is the largest even though it has the shortest length, which is the point of the comparison: a single dimension tells you nothing about volume on its own, only the product of all three does. In part (b) a written conclusion is required as well as the numbers; stopping at \(1620\) without stating that it is the largest would not complete the demonstration.