Higher November 2017 Paper 2 Q12
12. The diagram shows the aerial view of a hotel swimming pool.
Diagram not drawn to scale
A poster at the swimming pool gives the following information.
Diagram not drawn to scale
The swimming pool is filled to the top with water.
Calculate the possible volume of the water in the swimming pool. Give your answer in m3.
- You must state any assumption you make in calculating the volume.
- Show how this assumption impacts on your solution. [6]
| Scheme | Marks | Comments |
|---|---|---|
| Idea to work with the area of the cross-section × width of the pool | S1 | |
| Area of the cross-section, e.g. trapezium \(\tfrac12(1.4 + 2.2) \times 20\), or 2 rectangles \(x \times 1.4 + (20 - x) \times 2.2\) where \(x\) is a value used \(\lt 20\), or other more complex split of areas | M1 | Candidates may split the area into a number of trapezia or rectangles Allow 1 slip or 1 error |
| Area of cross-section \(\times\ 12\) | m1 | |
| Volume, e.g. Using: Trapezium or 2 rectangles \(x = 10\) 432 (m3), Two rectangles \(x = 8\) 451.2 (m3), Two rectangles \(x = 12\) 412.8 (m3) | A1 | Volume calculated correctly Do not FT from 1 slip or 1 error Two rectangles \(x = 1\) 518.4 (m3) Two rectangles \(x = 19\) 345.6 (m3) |
| Assumption, e.g. correct description of the pool floor used, i.e. cross-section is a trapezium or split into rectangles, OR e.g. correct description of the sides being vertical | E1 | FT provided S1 awarded |
| Showing or describing the impact of the assumption, with the actual volume possibly being the same or greater or less than the one calculated | E1 | FT provided S1 awarded |
| (6) |