Higher June 2025 Paper 2 Q8
8. A wooden block is shown below.
Zachary saws off a small block that is 30% of the original wooden block.
Diagrams not drawn to scale
The mass of Zachary’s small block is 5·4 kg.
The density of the wood is 0·75 g/cm3.
(a) Calculate the volume of the original wooden block. [5]
(b) Zachary converts the volume of the wooden block from cubic centimetres (cm3) to cubic inches (in3).
He uses the conversion 2·5 cm ≈ 1 inch.
Zachary says,“To convert the volume from cm3 into in3 I must divide the volume by 2·5.”Explain why Zachary’s method is incorrect. [1]
He uses the conversion 2·5 cm ≈ 1 inch.
Zachary says,“To convert the volume from cm3 into in3 I must divide the volume by 2·5.”Explain why Zachary’s method is incorrect. [1]
| Scheme | Marks | Comments |
|---|---|---|
| (Volume of original block =) 5.4 × 1000 | M1 | May be seen in any order and may follow an incorrect stage |
| \(\div\ 0.75\) | M1 | |
| \(\div\ 3 \times 10\) or \(\div\ 0.3\) | M1 | or equivalent e.g. \(\div 30 \times 100\) |
| = 24000 (cm3) | A2 | A1 for correct evaluation for two of the three calculations starting with 5.4.
|
| Scheme | Marks | Comments |
|---|---|---|
| A valid explanation e.g. ‘He should have divided by 2.53.’ ‘He should have divided by 15.625.’ ‘He should have cubed the 2.5.’ ‘He should have divided by 2.5 three times.’ | E1 | Allow e.g. ‘He should have cubed it.’ ‘2.53’ ‘Because they are cubed units, (and not linear)’ ‘You have to divide by the cube.’ ‘He has used the length scale factor and not the volume scale factor.’ Do not accept e.g. ‘Because it is a cubic number’ ‘He needs to know how many cm3 make an in3.’ ‘Because they are volumes.’ |
| (6) |