Higher June 2023 Paper 6 Q15
15 Two bottles are mathematically similar.
The small bottle holds 0.5 litres and has a height of 35 cm.
The large bottle holds 2 litres.
Calculate the height of the large bottle. [4]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 55.5 to 55.6 nfww | 4 | M3 for \(35 \times \sqrt[3]{\frac{2}{0.5}}\) oe or \(35 \div \sqrt[3]{\frac{0.5}{2}}\) oe or M2 for \(\sqrt[3]{\frac{2}{0.5}}\) oe soi by 1.58 to 1.59 or \(\sqrt[3]{\frac{0.5}{2}}\) oe soi by 0.62 to 0.63 or \(\frac{h^3}{35^3} = \frac{2}{0.5}\) oe or M1 for \(\frac{2}{0.5}\) oe soi by 4 or \(\frac{0.5}{2}\) oe soi by \(\frac{1}{4}\) If 0 scored then SC1 for 140 as final answer | Accept 56 as final answer after M3 May see as length ratio, eg M2 for \(\sqrt[3]{2} : \sqrt[3]{0.5}\) soi by 1.2599(…) to 1.26 : 0.7937(…) to 0.794 May see as volume ratio, eg. M1 for 2 : 0.5 oe May also be seen as part of wrong approach eg. \(35 \times 4\) scores M1 |