IP1U13 HOT Q8

The figure shows a container that is a trapezoidal prism. The container is empty at first, and then is filled with water by a pipe with diameter \(10\) cm at a constant speed of \(6\)\(\mathrm{m/s}\).

1. Find volume of water filled into the container per second in litres/s, leaving your answer in terms of \(\pi \).
2. Hence, find the total time needed for the container to be completely filled, correcting your answer to \(2\) decimal places.

After \(t\) seconds, the depth of the water in the container is \(1.4\) m and the breadth of the water surface is \(2.3\) m.

3. Find the value of \(t\), correcting your answer to \(2\) decimal places.
4. Find the volume of empty space in the container at this moment.
5. Find the area of the water surface at this moment.

Source correction: the diagram’s \(2.1\text{ m}\) label is inconsistent with its other dimensions. The width at height \(1.4\text{ m}\) is \(1.6+(2.4-1.6)(1.4/1.6)=2.3\text{ m}\). Use this corrected width in parts (c)–(e).