The diagram shows the net of a cuboid measuring \(10\) cm by \(4\) cm by \(3\) cm. (a) Work out the total area of the net. [3] (b) Work out the volume of th...

(a) The net of a cuboid is its six rectangular faces laid flat, and opposite faces are identical, so they form three matching pairs.

The three different rectangles from edges \(10\) cm, \(4\) cm and \(3\) cm are \(10 \times 4 = 40\ \mathrm{cm}^2\), \(10 \times 3 = 30\ \mathrm{cm}^2\) and \(4 \times 3 = 12\ \mathrm{cm}^2\) [M1].

Doubling for the pairs: \(2 \times (40 + 30 + 12)\) [M1], which is \(2 \times 82 = 164\ \mathrm{cm}^2\) [A1]. This is also the surface area of the cuboid, since folding does not change area.

(b) Volume of a cuboid is the product of its three perpendicular edges: \(10 \times 4 \times 3\) [M1], giving \(120\ \mathrm{cm}^3\) [A1].

Watch the units, since they separate the two parts: multiplying two lengths gives an area in \(\mathrm{cm}^2\), while multiplying three gives a volume in \(\mathrm{cm}^3\). The commonest error in the first part is stopping at \(82\ \mathrm{cm}^2\), which counts only three of the six faces.