Higher June 2022 Paper 6 Q10
10 The diagram shows a triangular prism and a cube.
The ends of the prism are right-angled triangles with base 16 cm and height 12 cm.
The prism is 18 cm long.
The volume of the prism is equal to the volume of the cube.
Find the surface area of the cube.
You must show your working. [6]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 864 with correct working | 6 | M1 for \(\dfrac{12 \times 16}{2} \times 18\) A1 for 1728 or M1 for \(\dfrac{12 \times 16}{2}\) | “correct working” requires at least M1M1 Accept e.g. 12 × 8 × 18 or 96 × 18 Allow \(12^3 = 1728\) for M1A1 |
| AND M1 for \(\sqrt[3]{\textit{their } 1728}\) A1 for 12 | Their 1728 must be from correct method for volume of triangular prism | ||
| AND M1 for \(6 \times (\textit{their } 12)^2\) | Their 12 must come from use of volume of triangular prism and cube root | ||
| If 0, 1 or 2 scored, instead award SC3 for 864 as final answer with no working or insufficient working If 0 or M1 scored, instead award SC2 for 12 seen as dimension of cube or \((\sqrt[3]{3456})^2 \times 6\) soi 1371 to 1372 with no working or insufficient working If 0 scored, award SC1 for 1728 or \(\sqrt[3]{3456}\) soi 15.1[…] with no working or insufficient working | |||