Higher November 2022 Unit 2 Q1
1. A solid metal cylinder has a radius of 2·3 cm and a height of 5 cm.
Diagram not drawn to scale
The mass of the cylinder is 423·1 g.
Find the density of the metal.
Give your answer in g/cm3. [4]
| Scheme | Marks | Comments |
|---|---|---|
| (Volume of cylinder =) \(\pi \times 2{\cdot}3^2 \times 5\) | M1 | May be seen or implied in later working. |
| = 83(·095….) (cm3) or 26·45π | A1 | Accept an answer between 83 and 83·11 inclusive. |
| (Density of metal =) 423·1 ÷ 83(·095….) | M1 | FT 423·1 ÷ ‘their volume of cylinder’, provided not 5 or 2·3 (derived or stated). Ignore any attempt to change units (e.g. 423·1 ÷ 83 ÷ 1000). |
| Accept an answer between 5 and 5·1 (g/cm3) | A1 | Mark final answer. |
Alternative method
| Scheme | Marks | Comments |
|---|---|---|
| (Density of metal =) \(\dfrac{423{\cdot}1}{\pi \times 2{\cdot}3^2 \times 5}\) | M2 | Award M1 for sight of \(\pi \times 2{\cdot}3^2 \times 5\). |
| Accept an answer between 5 and 5·1 (g/cm3) | A2 | A1 for sight of 423.1/26.45π or 15.9(96…)/π or any other simplified fraction with one step left to carry out. |