Higher June 2023 Paper 1 Q15
15. A small tank is a cuboid. It has a square base of side 20 cm.
The tank contains some liquid but is not full.
Diagram not drawn to scale
More of the same type of liquid is added to the tank:
- The total mass of the liquid in the tank is now 5400 grams.
- The depth of the liquid has increased by 50%.
- The density of the liquid is 0·9 g/cm3.
Calculate the original depth of the liquid.
You must show all your working. [5]
| Scheme | Marks | Comments |
|---|---|---|
| (Original depth of liquid =) 5400 | ||
| ÷ 0·9 | M1 | Method marks may be awarded in any order |
| ÷ (20 × 20) | M1 | |
| \(\times\ \dfrac{2}{3}\) | M1 | |
| 10 (cm) | A2 | Award A1 for sight of any ONE of the following:
|
Alternative method
| Scheme | Marks | Comments |
|---|---|---|
| Let original depth = \(x\) \(20 \times 20 \times 1.5x\ (= 600x)\) | M2 | M1 for \(20 \times 20 \times h\ (= 400h)\) |
| \(0.9 = \dfrac{5400}{600x}\ \left(= \dfrac{9}{x}\right)\) | M1 A1 | M1 for \(0.9 = \dfrac{5400}{\text{‘their volume’}}\) |
| \(x = 10\) (cm) | A1 |
Alternative method 2
| Scheme | Marks | Comments |
|---|---|---|
| Let final depth = \(h\) \(20 \times 20 \times h\ (= 400h)\) | M1 | |
| \(0.9 = \dfrac{5400}{400h}\) | M1 A1 | M1 for \(0.9 = \dfrac{5400}{\text{‘their volume’}}\) |
| (original depth =) \(h \times \dfrac{2}{3}\) | M1 | |
| 10 (cm) | A1 |
| (5) |