Foundation November 2019 Paper 3 Q22
22 Here is a small cuboid and a cube.
Small cuboids and cubes are stacked in layers to make larger cuboids.
Here is a cuboid made with four layers.
The pattern is continued to make a cuboid with volume 336 cm3
How many cubes are used? [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| \(6 \times 2 \times 2\) or \(2 \times 2 \times 2 \times 3\) or 24 or \(6 \times 2 \times 2 + 2 \times 2 \times 2 \times 3\) or 48 | M1 | oe volume of one layer oe volume of two layers |
| \(336 \div\) their 24 or 14 or \(336 \div\) their 48 or 7 | M1dep | oe eg \(336 \div 2 \div\) their 24 |
| 21 | A1 | |
| Alternative method 2 | ||
| \(6 \times 2 \times 2 \times 2 + 2 \times 2 \times 2 \times 6\) or 96 | M1 | oe volume of four layers |
| \(336 \div\) their 96 or 3.5 | M1dep | oe |
| 21 | A1 | |
| Alternative method 3 | ||
| \(336 \div 2\) or 168 | M1 | oe total volume of all cubes |
| their \(168 \div (2 \times 2 \times 2)\) or their \(168 \div 8\) | M1dep | oe |
| 21 | A1 | |
| Alternative method 4 | ||
| \(6 \times 2 \times 2\) or \(2 \times 2 \times 2 \times 3\) or 24 or \(6 \times 2 \times 2 \times 2 + 2 \times 2 \times 2 \times 6\) or 96 | M1 | oe volume of one layer oe volume of four layers |
| \((336 -\) their \(96) \div\) their \(24 + 4\) or \(240 \div\) their \(24 + 4\) or 10 + 4 or 14 | M1dep | oe using volume of additional layers |
| 21 | A1 | |
Additional guidance
24, 48 and 96 must not come from area or perimeter calculations