2025 DSS PRELIMS P2 Q5

The diagram shows a solid made of a cuboid \(ABCDEFGH\) and a triangular prism \(EFGHIJ\), resting on level ground. \(AB=8\text{ m}\), \(BC=12\text{ m}\), \(AE=3\text{ m}\), \(EI=3\text{ m}\) and \(FI=7\text{ m}\).

1. Show that angle \(EFI=21.8^\circ\), correct to 1 decimal place.[3]
2. Find the volume of the solid, leaving your answer correct to 2 decimal places.[2]
3. Find the vertical height of \(I\) above the ground.[2]
4. Find the angle of elevation of \(J\) from \(B\).[4]