2023 BMSS EOY P2 Q13

The diagram shows a cuboid with width \(x\) cm.
The width of the cuboid is \(2.5\) cm less than its height.
The length of the cuboid is four times of its height.

1. Write down an expression, in terms of \(x\), for the length of the cuboid.[1]

2. The total surface area of the cuboid is \(325\) \(\mathrm{cm}^2\).

   Form an equation, in terms of \(x\), to represent this information and show that it simplifies to \[18x^2 + 65x - 275 = 0.\]

   [3]
3. Solve the equation \(18x^2 + 65x - 275 = 0\).[2]
4. Find the volume of the cuboid.[2]