Higher June 2018 Paper 1R Q9
9 Here is an empty pool in the shape of a cuboid.
Diagram NOT accurately drawn
The width of the pool is 3 m.
The length of the pool is 12 m.
The top of the pool is 2.5 m above the base of the pool.
Jeb is going to put water in the pool.
The level of the surface of the water will be 60 cm below the top of the pool.
Water flows into the pool at 400 litres per minute.
1 m3 = 1000 litres
How long will it take to fill the pool to 60 cm below the top of the pool?
Give your answer in hours and minutes.
(4)
| Scheme | Marks |
|---|---|
| 2.5 − 0.6 = 1.9 | M1 |
| 3 × 12 × “1.9” (= 68.4) | M1 |
| “68.4” × 1000 ÷ 400 (= 171 minutes) | M1 |
| 2 hours 51 minutes | A1 |
| (4) | |
| (4 marks) |
Notes
M1: for using length × width × height to find a volume
M1: for their volume × 1000 ÷ 400
| Scheme | Marks |
|---|---|
| 250 − 60 = 190 | M1 |
| 300 × 1200 × “190” (= \(6.84 \times 10^{7}\)) | M1 |
| \(\text{``}{6.84 \times 10^{7}}\text{''} \div 10^{6} \times 1000 \div 400\) (= 171 minutes) | M1 |
| 2 hours 51 minutes | A1 |
Notes
M1: for using length × width × height to find a volume
M1: for their volume ÷ \(10^{6}\) × 1000 ÷ 400