Foundation November 2022 Paper 3 Q25
25 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 \(6^2\) for \(6 \times 6\) and \(6^3\) for \(6 \times 6 \times 6\) and \(12^2\) for \(12 \times 12\)) \(4 \times (6 \times 12) + 2 \times (12 \times 12)\) or \(4 \times 2 \times (6 \times 6) + 2 \times 4 \times (6 \times 6)\) or \(8 \times (6 \times 6) + 8 \times (6 \times 6)\) or \(4 \times 6 \times (6 \times 6) - 8 \times (6 \times 6)\) or \(24 \times (6 \times 6) - 8 \times (6 \times 6)\) or \(16 \times (6 \times 6)\) [=576] | 2 | M1 for full method for surface area \(4 \times 72 + 2 \times 144\) or \(4 \times 2 \times 36 + 2 \times 4 \times 36\) or \(8 \times 36 + 8 \times 36\) \(24 \times 36 - 8 \times 36\) oe or \(16 \times 36\) | Brackets do not need to be shown 0 for 288 + 288 864 – 288 \(4 \times 6 \times 4 \times 6\) \(24 \times 24\) |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 12.5 nfww | 4 | M2 for \((2 \times 6 \times 6) + (4 \times 6 \times 24)\) oe or M1 for calculating the surface area of one or more faces of the cuboid AND M1 for \(\dfrac{\textit{their } 648}{576}\) [\(\times 100\)] oe or \(\dfrac{(\textit{their } 648) - 576}{576}\) [\(\times 100\)] oe Alternative method M2 for 16 and 18 [exposed faces] or M1 for 16 or 18 [exposed faces] AND M1 for \(\dfrac{\textit{their } 18}{\textit{their } 16}\) [\(\times 100\)] or \(\dfrac{\textit{their } 18 - \textit{their } 16}{\textit{their } 16}\) [\(\times 100\)] | soi by 72 + 576 or 648 e.g. \(6 \times 6\) soi by 36 \(6 \times 24\) soi by 144 Their 648 from attempt at surface area involving \(6 \times (6\) or \(24)\) soi by 1.125 or 112.5 soi by 0.125 oe may be \(\dfrac{72}{576}\) [\(\times 100\)] soi by 1.125 or 112.5 soi by 0.125 |