IP1U13 HOT Q9

The figure below shows a swimming pool that consists of two parts, the shallow cuboid part, where the depth is \(1.2\) m, and the deep trapezoidal-prism part, where the depth is from \(1.2\) m to \(3\) m. The two parts are equal in length (\(30\) m) and breadth (\(9\) m), and the two parts are connected such that water is filled and drained simultaneously into and out of the pool.

1. Find the volume of the shallow cuboid part and the deep trapezoidal-prism part, respectively. Hence, find the total volume of the whole swimming pool.
2. Given that the whole swimming pool is completely filled with water originally, for maintenance need, water is drained out at a constant rate of \(9\) m\(^{3}\) per minute. Find
   1. the amount of time after which the shallow cuboid part is completely drained,
   2. the amount of time after which the whole swimming pool is completely drained, and
   3. the depth of water (measured from the bottom of the deep part) after \(36\) minutes.
   4. Determine the type of the shape formed by the remaining water after \(90\) minutes.
3. After maintenance, water is refilled into the empty swimming pool at a constant rate of \(9\) m\(^{3}\) per minute. In the grid below, draw the graph of the depth, \(h\), of water with respect to time, \(t\). Approximately sketch the curved part and accurately draw the straight-line part of the graph, if there is any.