Higher November 2022 Paper 6 Q7
7 A child has four identical wooden cubes of side length 6 cm.
(a) They arrange the cubes in a 2 by 2 by 1 arrangement to form a cuboid.
Show that the surface area of the cuboid is 576 cm2. [2]
(b) The child rearranges the cubes in a 4 by 1 by 1 arrangement to form a different cuboid.
Calculate the percentage increase in surface area for this cuboid compared with the 2 by 2 by 1 cuboid. [4]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| Method must include dimensions (accept 62 for 6 × 6 and 63 for 6 × 6 × 6 and 122 for 12 × 12) 4 × (6 × 12) + 2 × (12 × 12) or 4 × 2 × (6 × 6) + 2 × 4 × (6 × 6) or 8 × (6 × 6) + 8 × (6 × 6) or 4 × 6 × (6 × 6) – 8 × (6 × 6) or 24 × (6 × 6) – 8 × (6 × 6) or 16 × (6 × 6) [=576] | 2 | M1 for full method for surface area 4 × 72 + 2 × 144 or 4 × 2 × 36 + 2 × 4 × 36 or 8 × 36 + 8 × 36 or 24 × 36 – 8 × 36 oe or 16 × 36 | Brackets do not need to be shown 0 for 288 + 288 864 – 288 4 × 6 × 4 × 6 24 × 24 |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 12.5 nfww | 4 | M2 for (2 × 6 × 6) + (4 × 6 × 24) oe or M1 for calculating the surface area of one or more faces of the cuboid AND M1 for \(\frac{their\ 648}{576}\) [× 100] oe or \(\frac{(their\ 648) - 576}{576}\) [× 100] oe Alternative method M2 for 16 and 18 [exposed faces] or M1 for 16 or 18 [exposed faces] AND M1 for \(\frac{their\ 18}{their\ 16}\) [×100] or \(\frac{their\ 18 - their\ 16}{their\ 16}\) [×100] | soi by 72 + 576 or 648 e.g. 6 × 6 soi by 36 6 × 24 soi by 144 Their 648 from attempt at surface area involving 6 × (6 or 24) soi by 1.125 or 112.5 soi by 0.125 oe may be \(\frac{72}{576}\) [× 100] soi by 1.125 or 112.5 soi by 0.125 |