Higher November 2022 Paper 2 Q9
9. The diagram shows the interior length, width and height of a wooden crate.
Diagram not drawn to scale
Jake fills the crate with solid beeswax cylinders. They each have a length of 32 cm.
The cylinders fit tightly in the crate with 8 cylinders in each row.
The first two rows are shown in the diagram.
Jake continues to fill the crate in this way.
The density of the beeswax is 0·961 g/cm3.
Jake calculates the total mass of the cylinders to be more than 70 kg.
Is he correct?
Yes ☐ No ☐
Show how you decide. [7]
| Scheme | Marks | Comments |
|---|---|---|
| Multiplications can take place in any order | ||
| (Radius of cylinder =) 3 (cm) si | B1 | May be implied by e.g. \(d\) = 6 |
| (Number of cylinders in crate =) 80 | B1 | May be implied in later working |
| \(\pi \times 3^2 \times 32\) | M1 | (288π or 904.7(7..) to 904.9 cm3) |
| \(\times\, 0.961\) | M1 | (869.4 to 869.6(0…) g) FT ‘their derived volume’ providing it is a multiple of π. May use 0.000 961 (kg/cm3); allow multiplication by figs 961 if a unit conversion error |
| \(\times\, 80\) | M1 | FT ‘their 80’ × ‘their derived volume or mass’ |
| = 69 552 to 69 569 (g) | A1 | CAO |
| No indicated (with sight of 69(. ) kg or 70 000 g) | A1 | FT ‘their 69 552 to 69 569 (g)’ providing at least M2 previously awarded and no incorrect conversion to kg seen |
Alternative method
| Scheme | Marks | Comments |
|---|---|---|
| (Radius of cylinder =) 3 (cm) si | B1 | May be implied by e.g. \(d\) = 6 |
| (Number of cylinders in crate =) 80 | B1 | May be implied in later working |
| \(\pi \times 3^2 \times 32\) | M1 | (288π or 904.7(7..) to 904.9 cm3) |
| \(\times\, 0.961\) | M1 | (869.4 to 869.6(0…) g) FT ‘their derived volume’ providing it is a multiple of π. May use 0.000 961 (kg/cm3); allow multiplication by figs 961 if a unit conversion error |
| = 869.5 to 869.7(g) | A1 | FT ‘their 6 ÷ 2’ and possibly figs 961 Allow e.g. 870 if correct working seen |
| 70 000 ÷ 80 (= 875 (g)) | M1 | |
| No indicated (with sight of 869(. ) g and 875 g) | A1 | FT ‘their 869.5 to 869.7(g)’ or ‘their 870’ providing at least M2 previously awarded |
| (7) |