Higher November 2024 Paper 2 Q12
12 The diagram shows a solid cylinder with base radius 3 cm and height 8 cm.
It also shows a solid cube with side length \(h\) cm.
The cylinder is made from steel with a density of 7.86 g/cm3
The cube is made from brass with a density of 8.5 g/cm3
The mass of the cylinder is equal to the mass of the cube.
Work out the value of \(h\).
Give your answer correct to 1 decimal place. (5)
| Answer | Mark | Mark scheme |
|---|---|---|
| 5.9 | P1 | for a process to find the volume of the cylinder, eg \(\pi \times 3^2 \times 8\ (= 226.19\ldots)\) |
| P1 | for process to find mass of cylinder, eg \(\text{``}226.19\text{''} \times 7.86\ (= 1777.89\ldots)\) or \([\text{volume}_1] \times 7.86\) | |
| P1 | for process to find volume of cube, eg \(\text{``}1777.89\text{''} \div 8.5\ (= 209.16\ldots)\) or \([\text{mass}] \div 8.5\) | |
| P1 | for process to find side length, eg \(\sqrt[3]{\text{``}209.16\ldots\text{''}}\) or \(\sqrt[3]{[\text{volume}_2]}\) | |
| A1 | for answer in range 5.9 to 5.94 |
Additional guidance
Can be implied by \(72\pi\)
[volume1] must be unambiguously the volume of the cylinder but cannot be 3 or 8
[mass] must be unambiguously the mass of the cylinder
[volume2] must be unambiguously the volume of the cube