Volume Transfer Between Composite Solids

In a restaurant, the fruit punch is mixed in a container with no lid as shown in Figure 1. The container is a prism whose cross-section is a trapezium. The lengths of the parallel sides of the trapezium are \(10\) cm and \(15\) cm and the distance between the parallel sides is \(9\) cm. It is given that the capacity of the container is \(1.8\) litres.

1. Show that the height of the container is \(16\) cm.

All the fruit punch in one full container is transferred to a jar as shown in Figure 2.

The jar is made by joining a hemisphere of radius \(8\) cm to a part of a right circular cone of height, \(h\) cm.

2. Given that the slant height of the cone is \(17\) cm, show that \(h=15\) cm.
3. Find the depth of the fruit punch in this jar after all the fruit punch has been transferred from the container in Figure 1.