2022 TJC IP1 EOY Q12

The figure below (not drawn to scale) shows a solid prism. The cross-section of the prism consists of an isosceles trapezium, \(ABCD\), of height \(4\text{ cm}\), removed from a semicircle of diameter \(30\text{ cm}\). It is given that \(AB=CD=5\text{ cm}\), \(AD=14\text{ cm}\) and \(BC=8\text{ cm}\). The length of the prism is \(25\text{ cm}\).

1. Show that the area of the cross-section is \((112.5\pi-44)\text{ cm}^2\).[2]
2. Find, giving your answer correct to \(1\) decimal place, the volume of the prism.[1]
3. Find, giving your answer correct to \(1\) decimal place, the total surface area of the prism.[3]